Water Rocket

Author: Bernardo Bahia Monteiro (bbahia@umich.edu)

In this example, we will optimize a water rocket for range and height at the apogee, using design variables that are easily modifiable just before launch: the empty mass, the initial water volume and the launch angle. This example builds on multi-phase cannonball ane is adapted from Optimization of a Water Rocket in OpenMDAO/Dymos [BM20].

Nomenclature

Symbol	definition
\(v_\text{out}\)	water exit speed at the nozzle
\(A_\text{out}\)	nozzle area
\(V_w\)	water volume in the rocket
\(p\)	pressure in the rocket
\(p_a\)	ambient pressure
\(\dot{\,}\)	time derivative
\(k\)	polytropic constant
\(V_b\)	internal volume of the rocket
\(\rho_w\)	water density
\(T\)	thrust
\(q\)	dynamic pressure
\(S\)	cross sectional area
\((\cdot)_0\)	value of \((\cdot)\) at \(t=0\)
\(t\)	time

Problem Formulation

A natural objective function for a water rocket is the maximum height achieved by the rocket during flight, or the horizontal distance it travels, i.e. its range. The design of a water rocket is somewhat constrained by the soda bottle used as its engine. This means that the volume available for water and air is fixed, the initial launch pressure is limited by the bottle’s strength (since the pressure is directly related to the energy available for the rocket, it is easy to see that it should be as high as possible) and the nozzle throat area is also fixed. Given these manufacturing constraints, the design variables we are left with are the empty mass (it can be easily changed through adding ballast), the water volume at the launch, and the launch angle. With this considerations in mind, a natural formulation for the water rocket problem is

(84)\[\begin{align} \text{maximize} &\quad \text{range or height} \\ \text{w.r.t.} &\quad \text{empty mass, initial water volume, launch angle, trajectory} \\ \text{subject to} &\quad \text{flight dynamics} \\ &\quad \text{fluid dynamics inside the rocket} \\ &\quad 0 < \text{initial water volume} < \text{volume of bottle} \\ &\quad 0^\circ < \text{launch angle} < 90^\circ \\ &\quad 0 < \text{empty mass} \end{align}\]

Model

The water rocket model is divided into three basic components: a water engine, responsible for modelling the fluid dynamics inside the rocket and returning its thrust; the aerodynamics, responsible for calculating the atmospheric drag of the rocket; and the equations of motion, responsible for propagating the rocket’s trajectory in time, using Newton’s laws and the forces provided by the other two components.

In order to integrate these three basic components, some additional interfacing components are necessary: an atmospheric model to provide values of ambient pressure for the water engine and air density to the calculation of the dynamic pressure for the aerodynamic model, and a component that calculates the instantaneous mass of the rocket by summing the water mass with the rocket’s empty mass. The high level layout of this model is shown in below.

N2 diagram for the water rocket model

atmos, dynamic_pressure, aero and eom are the same models used in multi-phase cannonball. The remaining components are discussed below.

Warning

The eom component has a singularity in the flight path angle derivative when the flight speed is zero. This happens because the rotational dynamics are not modelled. This can cause convergence problems if the launch velocity is set to zero or the launch angle is set to \(90^\circ\)

Note

Since the range of altitudes achieved by the water rocket is very small (100m), the air density and pressure are practically constant, thus the use of an atmospheric model is not necessary. However, using it makes it easier to reuse code from [multi-phase cannonball (../multi_phase_cannonball/multi_phase_cannonball.md).

Water engine

The water engine is modelled by assuming that the air expansion in the rocket follows an adiabatic process and the water flow is incompressible and inviscid, i.e. it follows Bernoulli’s equation. We also make the following simplifying assumptions:

1. The thrust developed after the water is depleted is negligible

2. The area inside the bottle is much smaller than the nozzle area

3. The inertial forces do not affect the fluid dynamics inside the bottle

This simplified modelling can be found in Prusa[@Prusa2000]. A more rigorous formulation, which drops all these simplifying assumptions can be found in Wheeler[@Wheeler2002], Gommes[@Gommes2010], and Barria-Perotti[@BarrioPerotti2010].

The first assumption leads to an underestimation of the rocket performance, since the air left in the bottle after it is out of water is known to generate appreciable thrust[@Thorncroft2009]. This simplified model, however, produces physically meaningful results.

There are two states in this dynamical model, the water volume in the rocket \(V_w\) and the gauge pressure inside the rocket \(p\). The constitutive equations and the N2 diagram showing the model organization are shown below.

Constitutive equations of the water engine model

Component	Equation
water_exhaust_speed	\(v_\text{out} = \sqrt{2(p-p_a)/\rho_w}\)
water_flow_rate	\(\dot{V}_w = -v_\text{out} A_\text{out}\)
pressure_rate	\(\dot{p} = kp\frac{\dot{V_w}}{(V_b-V_w)}\)
water_thrust	\(T = (\rho_w v_\text{out})(v_\text{out}A_\text{out})\)

N2 diagram for the water engine group

import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt

import openmdao.api as om
import dymos as dm

class WaterEngine(om.Group):
    """
    Computes thrust and water flow for a water.

    Simplifications:
     - the pressure due to the water column in the non inertial frame (i.e.
       under a+g acceleration) is insignificant compared to the air pressure
     - the water does not have appreciable speed inside the bottle
    """
    def initialize(self):
        self.options.declare('num_nodes', types=int)

    def setup(self):
        nn = self.options['num_nodes']

        self.add_subsystem(name='water_exhaust_speed',
                           subsys=_WaterExhaustSpeed(num_nodes=nn),
                           promotes=['p', 'p_a', 'rho_w'])

        self.add_subsystem(name='water_flow_rate',
                           subsys=_WaterFlowRate(num_nodes=nn),
                           promotes=['A_out', 'Vdot'])

        self.add_subsystem(name='pressure_rate',
                           subsys=_PressureRate(num_nodes=nn),
                           promotes=['p', 'k', 'V_b', 'V_w', 'Vdot', 'pdot'])

        self.add_subsystem(name='water_thrust',
                           subsys=_WaterThrust(num_nodes=nn),
                           promotes=['rho_w', 'A_out', 'F'])

        self.connect('water_exhaust_speed.v_out', 'water_flow_rate.v_out')
        self.connect('water_exhaust_speed.v_out', 'water_thrust.v_out')

class _WaterExhaustSpeed(om.ExplicitComponent):
    def initialize(self):
        self.options.declare('num_nodes', types=int)

    def setup(self):
        nn = self.options['num_nodes']

        self.add_input(name='rho_w', val=1e3*np.ones(nn), desc='water density', units='kg/m**3')
        self.add_input(name='p', val=6.5e5*np.ones(nn), desc='air pressure', units='N/m**2')  # 5.5bar = 80 psi
        self.add_input(name='p_a', val=1.01e5*np.ones(nn), desc='air pressure', units='N/m**2')

        self.add_output(name='v_out', shape=(nn,), desc='water exhaust speed', units='m/s')

        ar = np.arange(nn)

        self.declare_partials(of='*', wrt='*', rows=ar, cols=ar)

    def compute(self, inputs, outputs):
        p = inputs['p']
        p_a = inputs['p_a']
        rho_w = inputs['rho_w']

        outputs['v_out'] = np.sqrt(2*(p-p_a)/rho_w)

    def compute_partials(self, inputs, partials):
        p = inputs['p']
        p_a = inputs['p_a']
        rho_w = inputs['rho_w']

        v_out = np.sqrt(2*(p-p_a)/rho_w)

        partials['v_out', 'p'] = 1/v_out/rho_w
        partials['v_out', 'p_a'] = -1/v_out/rho_w
        partials['v_out', 'rho_w'] = dv_outdrho_w = 1/v_out*(-(p-p_a)/rho_w**2)

class _PressureRate(om.ExplicitComponent):
    def initialize(self):
        self.options.declare('num_nodes', types=int)

    def setup(self):
        nn = self.options['num_nodes']

        self.add_input(name='p', val=np.ones(nn), desc='air pressure', units='N/m**2')
        self.add_input(name='k', val=1.4*np.ones(nn), desc='polytropic coefficient for expansion', units=None)
        self.add_input(name='V_b', val=2e-3*np.ones(nn), desc='bottle volume', units='m**3')
        self.add_input(name='V_w', val=1e-3*np.ones(nn), desc='water volume', units='m**3')
        self.add_input(name='Vdot', shape=(nn,), desc='water flow', units='m**3/s')

        self.add_output(name='pdot', shape=(nn,), desc='pressure derivative', units='N/m**2/s')

        ar = np.arange(nn)

        self.declare_partials(of='*', wrt='*', rows=ar, cols=ar)

    def compute(self, inputs, outputs):
        p = inputs['p']
        k = inputs['k']
        V_b = inputs['V_b']
        V_w = inputs['V_w']
        Vdot = inputs['Vdot']

        pdot = p*k*Vdot/(V_b-V_w)

        outputs['pdot'] = pdot

    def compute_partials(self, inputs, partials):
        p = inputs['p']
        k = inputs['k']
        V_b = inputs['V_b']
        V_w = inputs['V_w']
        Vdot = inputs['Vdot']

        partials['pdot', 'p'] = k*Vdot/(V_b-V_w)
        partials['pdot', 'k'] = p*Vdot/(V_b-V_w)
        partials['pdot', 'V_b'] = -p*k*Vdot/(V_b-V_w)**2
        partials['pdot', 'V_w'] = p*k*Vdot/(V_b-V_w)**2
        partials['pdot', 'Vdot'] = p*k/(V_b-V_w)

class _WaterFlowRate(om.ExplicitComponent):
    """ Computer water flow rate"""
    def initialize(self):
        self.options.declare('num_nodes', types=int)

    def setup(self):
        nn = self.options['num_nodes']

        self.add_input(name='A_out', val=np.ones(nn), desc='nozzle outlet area', units='m**2')
        self.add_input(name='v_out', val=np.zeros(nn), desc='water exhaust speed', units='m/s')

        self.add_output(name='Vdot', shape=(nn,), desc='water flow', units='m**3/s')

        ar = np.arange(nn)

        self.declare_partials(of='*', wrt='*', rows=ar, cols=ar)

    def compute(self, inputs, outputs):
        A_out = inputs['A_out']
        v_out = inputs['v_out']

        outputs['Vdot'] = -v_out*A_out

    def compute_partials(self, inputs, partials):
        A_out = inputs['A_out']
        v_out = inputs['v_out']

        partials['Vdot', 'A_out'] = -v_out
        partials['Vdot', 'v_out'] = -A_out

The _MassAdder component calculates the rocket’s instantaneous mass by summing the water mass with the rockets empty mass, i.e.

(85)\[\begin{align} m = m_\text{empty}+\rho_w V_w \end{align}\]

class _MassAdder(om.ExplicitComponent):

    def initialize(self):
        self.options.declare('num_nodes', types=int)

    def setup(self):
        nn = self.options['num_nodes']

        self.add_input('m_empty', val=np.zeros(nn), desc='empty mass', units='kg')
        self.add_input('V_w', val=1e-3*np.ones(nn), desc='water volume', units='m**3')
        self.add_input('rho_w', val=1e3*np.ones(nn), desc="water density", units='kg/m**3')

        self.add_output('m', val=np.zeros(nn), desc='total mass', units='kg')

        ar = np.arange(nn)
        self.declare_partials('*', '*', cols=ar, rows=ar)

    def compute(self, inputs, outputs):
        outputs['m'] = inputs['m_empty'] + inputs['rho_w']*inputs['V_w']

    def compute_partials(self, inputs, jacobian):
        jacobian['m', 'm_empty'] = 1
        jacobian['m', 'rho_w'] = inputs['V_w']
        jacobian['m', 'V_w'] = inputs['rho_w']

Now these components are joined in a single group

display_source('dymos.examples.water_rocket.water_propulsion_ode.WaterPropulsionODE')

class WaterPropulsionODE(om.Group):

    def initialize(self):
        self.options.declare('num_nodes', types=int)
        self.options.declare('ballistic', types=bool, default=False,
                             desc='If True, neglect propulsion system.')

    def setup(self):
        nn = self.options['num_nodes']

        self.add_subsystem(name='atmos',
                           subsys=USatm1976Comp(num_nodes=nn))

        if not self.options['ballistic']:
            self.add_subsystem(name='water_engine',
                               subsys=WaterEngine(num_nodes=nn),
                               promotes_inputs=['rho_w'])

            self.add_subsystem(name='mass_adder',
                               subsys=_MassAdder(num_nodes=nn),
                               promotes_inputs=['rho_w'])

        self.add_subsystem(name='dynamic_pressure',
                           subsys=DynamicPressureComp(num_nodes=nn))

        self.add_subsystem(name='aero',
                           subsys=LiftDragForceComp(num_nodes=nn))

        self.add_subsystem(name='eom',
                           subsys=FlightPathEOM2D(num_nodes=nn))

        self.connect('atmos.rho', 'dynamic_pressure.rho')
        self.connect('dynamic_pressure.q', 'aero.q')

        self.connect('aero.f_drag', 'eom.D')
        self.connect('aero.f_lift', 'eom.L')

        if not self.options['ballistic']:
            self.connect('atmos.pres', 'water_engine.p_a')
            self.connect('water_engine.F', 'eom.T')
            self.connect('mass_adder.m', 'eom.m')

Phases

The flight of the water rocket is split in three distinct phases: propelled ascent, ballistic ascent and ballistic descent. If the simplification of no thrust without water were lifted, there would be an extra “air propelled ascent” phase between the propelled ascent and ballistic ascent phases.

Propelled ascent: is the flight phase where the rocket still has water inside, and hence it is producing thrust. The thrust is given by the water engine model, and fed into the flight dynamic equations. It starts at launch and finishes when the water is depleted, i.e. \(V_w=0\).

Ballistic ascent: is the flight phase where the rocket is ascending (\(\gamma>0\)) but produces no thrust. This phase begins at the end of thepropelled ascent phase and ends at the apogee, defined by \(\gamma=0\).

Descent: is the phase where the rocket is descending without thrust. It begins at the end of the ballistic ascent phase and ends with ground impact, i.e. \(h=0\).

def new_propelled_ascent_phase(transcription):
    propelled_ascent = dm.Phase(ode_class=WaterPropulsionODE,
                                transcription=transcription)

    # All initial states except flight path angle and water volume are fixed
    # Final flight path angle is fixed (we will set it to zero so that the phase ends at apogee)
    # Final water volume is fixed (we will set it to zero so that phase ends when bottle empties)
    propelled_ascent.set_time_options(
        fix_initial=True, duration_bounds=(0.001, 0.5), duration_ref=0.1, units='s')
    propelled_ascent.add_state('r', units='m', rate_source='eom.r_dot',
                               fix_initial=True, fix_final=False, ref=100.0, defect_ref=100.0)
    propelled_ascent.add_state('h', units='m', rate_source='eom.h_dot', targets=['atmos.h'],
                               fix_initial=True, fix_final=False, ref=100.0, defect_ref=100.0)
    propelled_ascent.add_state('gam', units='deg', rate_source='eom.gam_dot', targets=['eom.gam'],
                               fix_initial=False, fix_final=False, lower=0, upper=85.0, ref=90)
    propelled_ascent.add_state('v', units='m/s', rate_source='eom.v_dot', targets=['dynamic_pressure.v', 'eom.v'],
                               fix_initial=True, fix_final=False, ref=100, defect_ref=100, lower=0.01)

    propelled_ascent.add_state('p', units='bar', rate_source='water_engine.pdot',
                               targets=['water_engine.p'], fix_initial=True, fix_final=False,
                               lower=1.02)
    propelled_ascent.add_state('V_w', units='L', rate_source='water_engine.Vdot',
                               targets=['water_engine.V_w', 'mass_adder.V_w'],
                               fix_initial=False, fix_final=True, ref=10, defect_ref=10,
                               lower=0)

    propelled_ascent.add_parameter(
        'S', targets=['aero.S'], units='m**2')
    propelled_ascent.add_parameter(
        'm_empty', targets=['mass_adder.m_empty'], units='kg')
    propelled_ascent.add_parameter(
        'V_b', targets=['water_engine.V_b'], units='m**3')

    propelled_ascent.add_timeseries_output('water_engine.F', 'T', units='N')

    return propelled_ascent

def new_ballistic_ascent_phase(transcription):
    ballistic_ascent = dm.Phase(ode_class=WaterPropulsionODE, transcription=transcription,
                                ode_init_kwargs={'ballistic': True})

    # All initial states are free (they will be  linked to the final stages of propelled_ascent).
    # Final flight path angle is fixed (we will set it to zero so that the phase ends at apogee)
    ballistic_ascent.set_time_options(
        fix_initial=False, initial_bounds=(0.001, 1), duration_bounds=(0.001, 10),
        duration_ref=1, units='s')

    ballistic_ascent.add_state('r', units='m', rate_source='eom.r_dot', fix_initial=False,
                               fix_final=False, ref=1.0, defect_ref=1.0)
    ballistic_ascent.add_state('h', units='m', rate_source='eom.h_dot', targets=['atmos.h'],
                               fix_initial=False, fix_final=False, ref=1.0)
    ballistic_ascent.add_state('gam', units='deg', rate_source='eom.gam_dot', targets=['eom.gam'],
                               fix_initial=False, fix_final=True, upper=89, ref=90)
    ballistic_ascent.add_state('v', units='m/s', rate_source='eom.v_dot',
                               targets=['dynamic_pressure.v', 'eom.v'], fix_initial=False,
                               fix_final=False, ref=1.)

    ballistic_ascent.add_parameter('S', targets=['aero.S'], units='m**2')
    ballistic_ascent.add_parameter('m_empty', targets=['eom.m'], units='kg')

    return ballistic_ascent

def new_descent_phase(transcription):
    descent = dm.Phase(ode_class=WaterPropulsionODE, transcription=transcription,
                       ode_init_kwargs={'ballistic': True})

    # All initial states and time are free (they will be linked to the final states of ballistic_ascent).
    # Final altitude is fixed (we will set it to zero so that the phase ends at ground impact)
    descent.set_time_options(initial_bounds=(.5, 100), duration_bounds=(.5, 100),
                             duration_ref=10, units='s')

    descent.add_state('r', units='m', rate_source='eom.r_dot', fix_initial=False, fix_final=False)
    descent.add_state('h', units='m', rate_source='eom.h_dot', targets=['atmos.h'],
                      fix_initial=False, fix_final=True)
    descent.add_state('gam', units='deg', rate_source='eom.gam_dot', targets=['eom.gam'],
                      fix_initial=False, fix_final=False)
    descent.add_state('v', units='m/s', rate_source='eom.v_dot',
                      targets=['dynamic_pressure.v', 'eom.v'],
                      fix_initial=False, fix_final=False,
                      ref=1)

    descent.add_parameter('S', targets=['aero.S'], units='m**2')
    descent.add_parameter('mass', targets=['eom.m'], units='kg')

    return descent

Model parameters

The model requires a few constant parameters. The values used are shown in the following table.

Values for parameters in the water rocket model

Parameter	Value	Unit	Reference
\(C_D\)	0.3450	-	[BPBMADiazFernandezO09]
\(S\)	\(\pi 106^2/4\)	\(mm^2\)	[BPBMADiazFernandezO09]
\(k\)	1.2	-	[TRP09] [FGH+20] [RBM13]
\(A_\text{out}\)	\(\pi22^2/4\)	\(mm^2\)	[air13]
\(V_b\)	2	L
\(\rho_w\)	1000	\(kg/m^3\)
\(p_0\)	6.5	bar
\(v_0\)	0.1	\(m/s\)
\(h_0\)	0	\(m\)
\(r_0\)	0	\(m\)

Values for the bottle volume \(V_b\), its cross-sectional area \(S\) and the nozzle area \(A_\text{out}\) are determined by the soda bottle that makes the rocket primary structure, and thus are not easily modifiable by the designer. The polytropic coefficient \(k\) is a function of the moist air characteristics inside the rocket. The initial speed \(v_0\) must be set to a value higher than zero, otherwise the flight dynamic equations become singular. This issue arises from the angular dynamics of the rocket not being modelled. The drag coefficient \(C_D\) is sensitive to the aerodynamic design, but can be optimized by a single discipline analysis. The initial pressure \(p_0\) should be maximized in order to obtain the maximum range or height for the rocket. It is limited by the structural properties of the bottle, which are modifiable by the designer, since the bottle needs to be available commercially. Finally, the starting point of the rocket is set to the origin.

Putting it all together

The different phases must be combined in a single trajectory, and linked in a sequence. Here we also define the design variables.

display_source('dymos.examples.water_rocket.phases.new_water_rocket_trajectory')

def new_water_rocket_trajectory(objective):
    tx_prop = dm.Radau(num_segments=50, order=3, compressed=True)
    tx_bal = dm.Radau(num_segments=10, order=3, compressed=True)
    tx_desc = dm.Radau(num_segments=10, order=3, compressed=True)
    traj = dm.Trajectory()

    # Add phases to trajectory
    propelled_ascent = traj.add_phase('propelled_ascent', new_propelled_ascent_phase(tx_prop))
    ballistic_ascent = traj.add_phase('ballistic_ascent', new_ballistic_ascent_phase(tx_bal))
    descent = traj.add_phase('descent', new_descent_phase(tx_desc))

    # Link phases
    traj.link_phases(phases=['propelled_ascent', 'ballistic_ascent'], vars=['*'])
    traj.link_phases(phases=['ballistic_ascent', 'descent'], vars=['*'])

    # Set objective function
    if objective == 'height':
        ballistic_ascent.add_objective('h', loc='final', ref=-1.0)
    elif objective == 'range':
        descent.add_objective('r', loc='final', ref=-100.0)
    else:
        raise ValueError(f"objective='{objective}' is not defined. Try using 'height' or 'range'")

    # Add design parameters to the trajectory.
    traj.add_parameter('CD',
                       targets={'propelled_ascent': ['aero.CD'],
                                'ballistic_ascent': ['aero.CD'],
                                'descent': ['aero.CD']},
                       val=0.3450, units=None, opt=False)
    traj.add_parameter('CL',
                       targets={'propelled_ascent': ['aero.CL'],
                                'ballistic_ascent': ['aero.CL'],
                                'descent': ['aero.CL']},
                       val=0.0, units=None, opt=False)
    traj.add_parameter('T',
                       targets={'ballistic_ascent': ['eom.T'],
                                'descent': ['eom.T']},
                       val=0.0, units='N', opt=False)
    traj.add_parameter('alpha',
                       targets={'propelled_ascent': ['eom.alpha'],
                                'ballistic_ascent': ['eom.alpha'],
                                'descent': ['eom.alpha']},
                       val=0.0, units='deg', opt=False)

    traj.add_parameter('m_empty', units='kg', val=0.15,
                       targets={'propelled_ascent': 'm_empty',
                                'ballistic_ascent': 'm_empty',
                                'descent': 'mass'},
                       lower=0.001, upper=1, ref=0.1,
                       opt=False)
    traj.add_parameter('V_b', units='m**3', val=2e-3,
                       targets={'propelled_ascent': 'V_b'},
                       opt=False)

    traj.add_parameter('S', units='m**2', val=np.pi*106e-3**2/4, opt=False)
    traj.add_parameter('A_out', units='m**2', val=np.pi*22e-3**2/4.,
                       targets={'propelled_ascent': ['water_engine.A_out']},
                       opt=False)
    traj.add_parameter('k', units=None, val=1.2, opt=False,
                       targets={'propelled_ascent': ['water_engine.k']})

    # Make parameter m_empty a design variable
    traj.set_parameter_options('m_empty', opt=True)

    return traj, {'propelled_ascent': propelled_ascent,
                  'ballistic_ascent': ballistic_ascent,
                  'descent': descent}

Helper Functions to Access the Results

from collections import namedtuple


def summarize_results(water_rocket_problem):
    p = water_rocket_problem
    Entry = namedtuple('Entry', 'value unit')
    summary = {
        'Launch angle': Entry(p.get_val('traj.propelled_ascent.timeseries.gam',  units='deg')[0, 0], 'deg'),
        'Flight angle at end of propulsion': Entry(p.get_val('traj.propelled_ascent.timeseries.gam',
                                                   units='deg')[-1, 0], 'deg'),
        'Empty mass': Entry(p.get_val('traj.parameters:m_empty', units='kg')[0], 'kg'),
        'Water volume': Entry(p.get_val('traj.propelled_ascent.timeseries.V_w', 'L')[0, 0], 'L'),
        'Maximum range': Entry(p.get_val('traj.descent.timeseries.r', units='m')[-1, 0], 'm'),
        'Maximum height': Entry(p.get_val('traj.ballistic_ascent.timeseries.h', units='m')[-1, 0], 'm'),
        'Maximum velocity': Entry(p.get_val('traj.propelled_ascent.timeseries.v', units='m/s')[-1, 0], 'm/s'),
    }

    return summary

colors={'pa': 'tab:blue', 'ba': 'tab:orange', 'd': 'tab:green'}


def plot_propelled_ascent(p, exp_out):
    fig, ax = plt.subplots(2, 2, sharex=True, figsize=(12, 6))
    t_imp = p.get_val('traj.propelled_ascent.timeseries.time', 's')
    t_exp = exp_out.get_val('traj.propelled_ascent.timeseries.time', 's')
    
    c = colors['pa']

    ax[0,0].plot(t_imp, p.get_val('traj.propelled_ascent.timeseries.p', 'bar'), '.', color=c)
    ax[0,0].plot(t_exp, exp_out.get_val('traj.propelled_ascent.timeseries.p', 'bar'), '-', color=c)
    ax[0,0].set_ylabel('p (bar)')
    ax[0,0].set_ylim(bottom=0)

    ax[1,0].plot(t_imp, p.get_val('traj.propelled_ascent.timeseries.V_w', 'L'), '.', color=c)
    ax[1,0].plot(t_exp, exp_out.get_val('traj.propelled_ascent.timeseries.V_w', 'L'), '-', color=c)
    ax[1,0].set_ylabel('$V_w$ (L)')

    ax[0,1].plot(t_imp, p.get_val('traj.propelled_ascent.timeseries.T', 'N'), '.', color=c)
    ax[0,1].plot(t_exp, exp_out.get_val('traj.propelled_ascent.timeseries.T', 'N'), '-', color=c)
    ax[0,1].set_ylabel('T (N)')
    ax[0,1].set_ylim(bottom=0)

    ax[1,1].plot(t_imp, p.get_val('traj.propelled_ascent.timeseries.v', 'm/s'), '.', color=c)
    ax[1,1].plot(t_exp, exp_out.get_val('traj.propelled_ascent.timeseries.v', 'm/s'), '-', color=c)
    ax[1,1].set_ylabel('v (m/s)')
    ax[1,1].set_ylim(bottom=0)

    ax[1,0].set_xlabel('t (s)')
    ax[1,1].set_xlabel('t (s)')
    
    for i in range(4):
        ax.ravel()[i].grid(True, alpha=0.2)

    fig.tight_layout()

def plot_states(p, exp_out, legend_loc='right', legend_ncol=3):
    fig, axes = plt.subplots(nrows=2, ncols=2, figsize=(12, 4), sharex=True)

    states = ['r', 'h', 'v', 'gam']
    units = ['m', 'm', 'm/s', 'deg']
    phases = ['propelled_ascent', 'ballistic_ascent', 'descent']

    time_imp = {'ballistic_ascent': p.get_val('traj.ballistic_ascent.timeseries.time'),
                'propelled_ascent': p.get_val('traj.propelled_ascent.timeseries.time'),
                'descent': p.get_val('traj.descent.timeseries.time')}

    time_exp = {'ballistic_ascent': exp_out.get_val('traj.ballistic_ascent.timeseries.time'),
                'propelled_ascent': exp_out.get_val('traj.propelled_ascent.timeseries.time'),
                'descent': exp_out.get_val('traj.descent.timeseries.time')}

    x_imp = {phase: {state: p.get_val(f"traj.{phase}.timeseries.{state}", unit)
                     for state, unit in zip(states, units)
                     }
             for phase in phases
             }

    x_exp = {phase: {state: exp_out.get_val(f"traj.{phase}.timeseries.{state}", unit)
                     for state, unit in zip(states, units)
                     }
             for phase in phases
             }

    for i, (state, unit) in enumerate(zip(states, units)):
        axes.ravel()[i].set_ylabel(f"{state} ({unit})" if state != 'gam' else f'$\gamma$ ({unit})')

        axes.ravel()[i].plot(time_imp['propelled_ascent'], x_imp['propelled_ascent'][state], '.', color=colors['pa'])
        axes.ravel()[i].plot(time_imp['ballistic_ascent'], x_imp['ballistic_ascent'][state], '.', color=colors['ba'])
        axes.ravel()[i].plot(time_imp['descent'], x_imp['descent'][state], '.', color=colors['d'])
        h1, = axes.ravel()[i].plot(time_exp['propelled_ascent'], x_exp['propelled_ascent'][state], '-', color=colors['pa'], label='Propelled Ascent')
        h2, = axes.ravel()[i].plot(time_exp['ballistic_ascent'], x_exp['ballistic_ascent'][state], '-', color=colors['ba'], label='Ballistic Ascent')
        h3, = axes.ravel()[i].plot(time_exp['descent'], x_exp['descent'][state], '-', color=colors['d'], label='Descent')

        if state == 'gam':
            axes.ravel()[i].yaxis.set_major_locator(mpl.ticker.MaxNLocator(nbins='auto', steps=[1, 1.5, 3, 4.5, 6, 9, 10]))
            axes.ravel()[i].set_yticks(np.arange(-90, 91, 45))
        
        axes.ravel()[i].grid(True, alpha=0.2)

    axes[1, 0].set_xlabel('t (s)')
    axes[1, 1].set_xlabel('t (s)')
    
    plt.figlegend(handles=[h1, h2, h3], loc=legend_loc, ncol=legend_ncol)

    fig.tight_layout()

def plot_trajectory(p, exp_out, legend_loc='center right'):
    fig, axes = plt.subplots(nrows=1, ncols=1, figsize=(8, 6))

    time_imp = {'ballistic_ascent': p.get_val('traj.ballistic_ascent.timeseries.time'),
                'propelled_ascent': p.get_val('traj.propelled_ascent.timeseries.time'),
                'descent': p.get_val('traj.descent.timeseries.time')}

    time_exp = {'ballistic_ascent': exp_out.get_val('traj.ballistic_ascent.timeseries.time'),
                'propelled_ascent': exp_out.get_val('traj.propelled_ascent.timeseries.time'),
                'descent': exp_out.get_val('traj.descent.timeseries.time')}

    r_imp = {'ballistic_ascent': p.get_val('traj.ballistic_ascent.timeseries.r'),
             'propelled_ascent': p.get_val('traj.propelled_ascent.timeseries.r'),
             'descent': p.get_val('traj.descent.timeseries.r')}

    r_exp = {'ballistic_ascent': exp_out.get_val('traj.ballistic_ascent.timeseries.r'),
             'propelled_ascent': exp_out.get_val('traj.propelled_ascent.timeseries.r'),
             'descent': exp_out.get_val('traj.descent.timeseries.r')}

    h_imp = {'ballistic_ascent': p.get_val('traj.ballistic_ascent.timeseries.h'),
             'propelled_ascent': p.get_val('traj.propelled_ascent.timeseries.h'),
             'descent': p.get_val('traj.descent.timeseries.h')}

    h_exp = {'ballistic_ascent': exp_out.get_val('traj.ballistic_ascent.timeseries.h'),
             'propelled_ascent': exp_out.get_val('traj.propelled_ascent.timeseries.h'),
             'descent': exp_out.get_val('traj.descent.timeseries.h')}

    axes.plot(r_imp['propelled_ascent'], h_imp['propelled_ascent'], 'o', color=colors['pa'])
    axes.plot(r_imp['ballistic_ascent'], h_imp['ballistic_ascent'], 'o', color=colors['ba'])
    axes.plot(r_imp['descent'], h_imp['descent'], 'o', color=colors['d'])

    h1, = axes.plot(r_exp['propelled_ascent'], h_exp['propelled_ascent'], '-', color=colors['pa'], label='Propelled Ascent')
    h2, = axes.plot(r_exp['ballistic_ascent'], h_exp['ballistic_ascent'], '-', color=colors['ba'], label='Ballistic Ascent')
    h3, = axes.plot(r_exp['descent'], h_exp['descent'], '-', color=colors['d'], label='Descent')

    axes.set_xlabel('r (m)')
    axes.set_ylabel('h (m)')
    axes.set_aspect('equal', 'box')
    plt.figlegend(handles=[h1, h2, h3], loc=legend_loc)
    axes.grid(alpha=0.2)

    fig.tight_layout()

Optimizing for Height

from dymos.examples.water_rocket.phases import new_water_rocket_trajectory, set_sane_initial_guesses

p = om.Problem(model=om.Group())

traj, phases = new_water_rocket_trajectory(objective='height')
traj = p.model.add_subsystem('traj', traj)

p.driver = om.pyOptSparseDriver(optimizer='IPOPT', print_results=False)
p.driver.opt_settings['print_level'] = 4
p.driver.opt_settings['max_iter'] = 1000
p.driver.opt_settings['mu_strategy'] = 'monotone'
p.driver.declare_coloring(tol=1.0E-12)

# Finish Problem Setup
p.model.linear_solver = om.DirectSolver()

p.setup()
set_sane_initial_guesses(p, phases)

dm.run_problem(p, run_driver=True, simulate=True)

summary = summarize_results(p)
for key, entry in summary.items():
    print(f'{key}: {entry.value:6.4f} {entry.unit}')
    
sol_out = om.CaseReader('dymos_solution.db').get_case('final')
sim_out = om.CaseReader('dymos_simulation.db').get_case('final')

--- Constraint Report [traj] ---
    --- propelled_ascent ---
        None
    --- ballistic_ascent ---
        None
    --- descent ---
        None

Model viewer data has already been recorded for Driver.
Model viewer data has already been recorded for Driver.

Full total jacobian was computed 3 times, taking 2.401078 seconds.
Total jacobian shape: (1151, 1153) 

Jacobian shape: (1151, 1153)  ( 0.67% nonzero)
FWD solves: 20   REV solves: 0
Total colors vs. total size: 20 vs 1153  (98.3% improvement)

Sparsity computed using tolerance: 1e-12
Time to compute sparsity: 2.401078 sec.
Time to compute coloring: 2.243142 sec.
Memory to compute coloring: -20.132812 MB.

List of user-set options:

                                    Name   Value                used
                        file_print_level = 5                     yes
                   hessian_approximation = limited-memory        yes
                           linear_solver = mumps                 yes
                                max_iter = 1000                  yes
                             mu_strategy = monotone              yes
                      nlp_scaling_method = user-scaling          yes
                             output_file = IPOPT.out             yes
                             print_level = 4                     yes
                      print_user_options = yes                   yes
                                      sb = yes                   yes
Total number of variables............................:     1153
                     variables with only lower bounds:      450
                variables with lower and upper bounds:      157
                     variables with only upper bounds:       30
Total number of equality constraints.................:     1150
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

Number of Iterations....: 61

                                   (scaled)                 (unscaled)
Objective...............:  -5.3408199947689909e+01   -5.3408199947689909e+01
Dual infeasibility......:   4.6055177795796835e-09    4.6055177795796835e-09
Constraint violation....:   2.4743727268044590e-09    2.4743727268044590e-09
Variable bound violation:   9.8625653199846397e-09    9.8625653199846397e-09
Complementarity.........:   2.5059035596800862e-09    2.5059035596800862e-09
Overall NLP error.......:   4.6055177795796835e-09    4.6055177795796835e-09


Number of objective function evaluations             = 94
Number of objective gradient evaluations             = 62
Number of equality constraint evaluations            = 94
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 62
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 0
Total seconds in IPOPT                               = 9.508

EXIT: Optimal Solution Found.

Simulating trajectory traj
Model viewer data has already been recorded for Driver.

Done simulating trajectory traj

Launch angle: 85.0000 deg
Flight angle at end of propulsion: 84.0887 deg
Empty mass: 0.1449 kg
Water volume: 0.9836 L
Maximum range: 16.0259 m
Maximum height: 53.4082 m
Maximum velocity: 46.1530 m/s

Maximum Height Solution: Propulsive Phase

plot_propelled_ascent(sol_out, sim_out)

Maximum Height Solution: Height vs. Range

Note that the equations of motion used here are singular in vertical flight, so the launch angle (the initial flight path angle) was limited to 85 degrees.

plot_trajectory(sol_out, sim_out, legend_loc='center right')

Maximum Height Solution: State History

plot_states(sol_out, sim_out, legend_loc='lower center', legend_ncol=3)

Optimizing for Range

from dymos.examples.water_rocket.phases import new_water_rocket_trajectory, set_sane_initial_guesses

p = om.Problem(model=om.Group())

traj, phases = new_water_rocket_trajectory(objective='range')
traj = p.model.add_subsystem('traj', traj)

p.driver = om.pyOptSparseDriver(optimizer='IPOPT')
p.driver.opt_settings['print_level'] = 4
p.driver.opt_settings['max_iter'] = 1000
p.driver.opt_settings['mu_strategy'] = 'monotone'
p.driver.declare_coloring(tol=1.0E-12)

# Finish Problem Setup
p.model.linear_solver = om.DirectSolver()

p.setup()
set_sane_initial_guesses(p, phases)

dm.run_problem(p, run_driver=True, simulate=True)

summary = summarize_results(p)
for key, entry in summary.items():
    print(f'{key}: {entry.value:6.4f} {entry.unit}')

sol_out = om.CaseReader('dymos_solution.db').get_case('final')
sim_out = om.CaseReader('dymos_simulation.db').get_case('final')

--- Constraint Report [traj] ---
    --- propelled_ascent ---
        None
    --- ballistic_ascent ---
        None
    --- descent ---
        None

/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/recorders/sqlite_recorder.py:227: UserWarning:The existing case recorder file, dymos_solution.db, is being overwritten.

Model viewer data has already been recorded for Driver.
Model viewer data has already been recorded for Driver.

Full total jacobian was computed 3 times, taking 2.378550 seconds.
Total jacobian shape: (1151, 1153) 

Jacobian shape: (1151, 1153)  ( 0.67% nonzero)
FWD solves: 20   REV solves: 0
Total colors vs. total size: 20 vs 1153  (98.3% improvement)

Sparsity computed using tolerance: 1e-12
Time to compute sparsity: 2.378550 sec.
Time to compute coloring: 2.255864 sec.
Memory to compute coloring: 0.000000 MB.

List of user-set options:

                                    Name   Value                used
                        file_print_level = 5                     yes
                   hessian_approximation = limited-memory        yes
                           linear_solver = mumps                 yes
                                max_iter = 1000                  yes
                             mu_strategy = monotone              yes
                      nlp_scaling_method = user-scaling          yes
                             output_file = IPOPT.out             yes
                             print_level = 4                     yes
                      print_user_options = yes                   yes
                                      sb = yes                   yes
Total number of variables............................:     1153
                     variables with only lower bounds:      450
                variables with lower and upper bounds:      157
                     variables with only upper bounds:       30
Total number of equality constraints.................:     1150
Total number of inequality constraints...............:        0
        inequality constraints with only lower bounds:        0
   inequality constraints with lower and upper bounds:        0
        inequality constraints with only upper bounds:        0

Number of Iterations....: 45

                                   (scaled)                 (unscaled)
Objective...............:  -8.5111445102321892e-01   -8.5111445102321892e-01
Dual infeasibility......:   4.9960731512017345e-11    4.9960731512017345e-11
Constraint violation....:   3.3423372082394665e-09    3.3423372082394665e-09
Variable bound violation:   0.0000000000000000e+00    0.0000000000000000e+00
Complementarity.........:   9.0909098027636304e-10    9.0909098027636304e-10
Overall NLP error.......:   3.3423372082394665e-09    3.3423372082394665e-09


Number of objective function evaluations             = 55
Number of objective gradient evaluations             = 46
Number of equality constraint evaluations            = 55
Number of inequality constraint evaluations          = 0
Number of equality constraint Jacobian evaluations   = 46
Number of inequality constraint Jacobian evaluations = 0
Number of Lagrangian Hessian evaluations             = 0
Total seconds in IPOPT                               = 7.894

EXIT: Optimal Solution Found.


Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
    Objective Function: _objfunc

    Solution: 
--------------------------------------------------------------------------------
    Total Time:                    7.8963
       User Objective Time :       0.2656
       User Sensitivity Time :     5.8174
       Interface Time :            1.1200
       Opt Solver Time:            0.6933
    Calls to Objective Function :      55
    Calls to Sens Function :           46


   Objectives
      Index  Name                                                 Value
          0  traj.phases.descent.indep_states.states:r    -8.511145E-01

   Variables (c - continuous, i - integer, d - discrete)
      Index  Name                                                       Type      Lower Bound            Value      Upper Bound     Status
          0  traj.parameters:m_empty_0                                     c     1.000000E-02     1.891011E+00     1.000000E+01           
          1  traj.ballistic_ascent.t_initial_0                             c     1.000000E-03     1.126018E-01     1.000000E+00           
          2  traj.ballistic_ascent.t_duration_0                            c     1.000000E-03     1.928857E+00     1.000000E+01           
          3  traj.phases.ballistic_ascent.indep_states.states:r_0          c    -1.000000E+21     1.608068E+00     1.000000E+21           
          4  traj.phases.ballistic_ascent.indep_states.states:r_1          c    -1.000000E+21     3.795392E+00     1.000000E+21           
          5  traj.phases.ballistic_ascent.indep_states.states:r_2          c    -1.000000E+21     6.718919E+00     1.000000E+21           
          6  traj.phases.ballistic_ascent.indep_states.states:r_3          c    -1.000000E+21     7.622741E+00     1.000000E+21           
          7  traj.phases.ballistic_ascent.indep_states.states:r_4          c    -1.000000E+21     9.655603E+00     1.000000E+21           
          8  traj.phases.ballistic_ascent.indep_states.states:r_5          c    -1.000000E+21     1.238107E+01     1.000000E+21           
          9  traj.phases.ballistic_ascent.indep_states.states:r_6          c    -1.000000E+21     1.322554E+01     1.000000E+21           
         10  traj.phases.ballistic_ascent.indep_states.states:r_7          c    -1.000000E+21     1.512810E+01     1.000000E+21           
         11  traj.phases.ballistic_ascent.indep_states.states:r_8          c    -1.000000E+21     1.768560E+01     1.000000E+21           
         12  traj.phases.ballistic_ascent.indep_states.states:r_9          c    -1.000000E+21     1.847954E+01     1.000000E+21           
         13  traj.phases.ballistic_ascent.indep_states.states:r_10         c    -1.000000E+21     2.027084E+01     1.000000E+21           
         14  traj.phases.ballistic_ascent.indep_states.states:r_11         c    -1.000000E+21     2.268424E+01     1.000000E+21           
         15  traj.phases.ballistic_ascent.indep_states.states:r_12         c    -1.000000E+21     2.343468E+01     1.000000E+21           
         16  traj.phases.ballistic_ascent.indep_states.states:r_13         c    -1.000000E+21     2.512994E+01     1.000000E+21           
         17  traj.phases.ballistic_ascent.indep_states.states:r_14         c    -1.000000E+21     2.741840E+01     1.000000E+21           
         18  traj.phases.ballistic_ascent.indep_states.states:r_15         c    -1.000000E+21     2.813101E+01     1.000000E+21           
         19  traj.phases.ballistic_ascent.indep_states.states:r_16         c    -1.000000E+21     2.974250E+01     1.000000E+21           
         20  traj.phases.ballistic_ascent.indep_states.states:r_17         c    -1.000000E+21     3.192155E+01     1.000000E+21           
         21  traj.phases.ballistic_ascent.indep_states.states:r_18         c    -1.000000E+21     3.260091E+01     1.000000E+21           
         22  traj.phases.ballistic_ascent.indep_states.states:r_19         c    -1.000000E+21     3.413863E+01     1.000000E+21           
         23  traj.phases.ballistic_ascent.indep_states.states:r_20         c    -1.000000E+21     3.622089E+01     1.000000E+21           
         24  traj.phases.ballistic_ascent.indep_states.states:r_21         c    -1.000000E+21     3.687074E+01     1.000000E+21           
         25  traj.phases.ballistic_ascent.indep_states.states:r_22         c    -1.000000E+21     3.834281E+01     1.000000E+21           
         26  traj.phases.ballistic_ascent.indep_states.states:r_23         c    -1.000000E+21     4.033856E+01     1.000000E+21           
         27  traj.phases.ballistic_ascent.indep_states.states:r_24         c    -1.000000E+21     4.096196E+01     1.000000E+21           
         28  traj.phases.ballistic_ascent.indep_states.states:r_25         c    -1.000000E+21     4.237499E+01     1.000000E+21           
         29  traj.phases.ballistic_ascent.indep_states.states:r_26         c    -1.000000E+21     4.429259E+01     1.000000E+21           
         30  traj.phases.ballistic_ascent.indep_states.states:r_27         c    -1.000000E+21     4.489200E+01     1.000000E+21           
         31  traj.phases.ballistic_ascent.indep_states.states:r_28         c    -1.000000E+21     4.625134E+01     1.000000E+21           
         32  traj.phases.ballistic_ascent.indep_states.states:r_29         c    -1.000000E+21     4.809752E+01     1.000000E+21           
         33  traj.phases.ballistic_ascent.indep_states.states:r_30         c    -1.000000E+21     4.867492E+01     1.000000E+21           
         34  traj.phases.ballistic_ascent.indep_states.states:h_0          c    -1.000000E+21     1.304114E+00     1.000000E+21           
         35  traj.phases.ballistic_ascent.indep_states.states:h_1          c    -1.000000E+21     3.014264E+00     1.000000E+21           
         36  traj.phases.ballistic_ascent.indep_states.states:h_2          c    -1.000000E+21     5.225708E+00     1.000000E+21           
         37  traj.phases.ballistic_ascent.indep_states.states:h_3          c    -1.000000E+21     5.891330E+00     1.000000E+21           
         38  traj.phases.ballistic_ascent.indep_states.states:h_4          c    -1.000000E+21     7.355713E+00     1.000000E+21           
         39  traj.phases.ballistic_ascent.indep_states.states:h_5          c    -1.000000E+21     9.244599E+00     1.000000E+21           
         40  traj.phases.ballistic_ascent.indep_states.states:h_6          c    -1.000000E+21     9.811786E+00     1.000000E+21           
         41  traj.phases.ballistic_ascent.indep_states.states:h_7          c    -1.000000E+21     1.105688E+01     1.000000E+21           
         42  traj.phases.ballistic_ascent.indep_states.states:h_8          c    -1.000000E+21     1.265608E+01     1.000000E+21           
         43  traj.phases.ballistic_ascent.indep_states.states:h_9          c    -1.000000E+21     1.313444E+01     1.000000E+21           
         44  traj.phases.ballistic_ascent.indep_states.states:h_10         c    -1.000000E+21     1.418094E+01     1.000000E+21           
         45  traj.phases.ballistic_ascent.indep_states.states:h_11         c    -1.000000E+21     1.551628E+01     1.000000E+21           
         46  traj.phases.ballistic_ascent.indep_states.states:h_12         c    -1.000000E+21     1.591340E+01     1.000000E+21           
         47  traj.phases.ballistic_ascent.indep_states.states:h_13         c    -1.000000E+21     1.677769E+01     1.000000E+21           
         48  traj.phases.ballistic_ascent.indep_states.states:h_14         c    -1.000000E+21     1.786976E+01     1.000000E+21           
         49  traj.phases.ballistic_ascent.indep_states.states:h_15         c    -1.000000E+21     1.819170E+01     1.000000E+21           
         50  traj.phases.ballistic_ascent.indep_states.states:h_16         c    -1.000000E+21     1.888693E+01     1.000000E+21           
         51  traj.phases.ballistic_ascent.indep_states.states:h_17         c    -1.000000E+21     1.975227E+01     1.000000E+21           
         52  traj.phases.ballistic_ascent.indep_states.states:h_18         c    -1.000000E+21     2.000394E+01     1.000000E+21           
         53  traj.phases.ballistic_ascent.indep_states.states:h_19         c    -1.000000E+21     2.054074E+01     1.000000E+21           
         54  traj.phases.ballistic_ascent.indep_states.states:h_20         c    -1.000000E+21     2.119285E+01     1.000000E+21           
         55  traj.phases.ballistic_ascent.indep_states.states:h_21         c    -1.000000E+21     2.137823E+01     1.000000E+21           
         56  traj.phases.ballistic_ascent.indep_states.states:h_22         c    -1.000000E+21     2.176532E+01     1.000000E+21           
         57  traj.phases.ballistic_ascent.indep_states.states:h_23         c    -1.000000E+21     2.221529E+01     1.000000E+21           
         58  traj.phases.ballistic_ascent.indep_states.states:h_24         c    -1.000000E+21     2.233771E+01     1.000000E+21           
         59  traj.phases.ballistic_ascent.indep_states.states:h_25         c    -1.000000E+21     2.258232E+01     1.000000E+21           
         60  traj.phases.ballistic_ascent.indep_states.states:h_26         c    -1.000000E+21     2.283941E+01     1.000000E+21           
         61  traj.phases.ballistic_ascent.indep_states.states:h_27         c    -1.000000E+21     2.290162E+01     1.000000E+21           
         62  traj.phases.ballistic_ascent.indep_states.states:h_28         c    -1.000000E+21     2.300985E+01     1.000000E+21           
         63  traj.phases.ballistic_ascent.indep_states.states:h_29         c    -1.000000E+21     2.308194E+01     1.000000E+21           
         64  traj.phases.ballistic_ascent.indep_states.states:h_30         c    -1.000000E+21     2.308634E+01     1.000000E+21           
         65  traj.phases.ballistic_ascent.indep_states.states:gam_0        c    -1.111111E+19     4.265381E-01     9.888889E-01           
         66  traj.phases.ballistic_ascent.indep_states.states:gam_1        c    -1.111111E+19     4.182287E-01     9.888889E-01           
         67  traj.phases.ballistic_ascent.indep_states.states:gam_2        c    -1.111111E+19     4.060968E-01     9.888889E-01           
         68  traj.phases.ballistic_ascent.indep_states.states:gam_3        c    -1.111111E+19     4.020909E-01     9.888889E-01           
         69  traj.phases.ballistic_ascent.indep_states.states:gam_4        c    -1.111111E+19     3.926065E-01     9.888889E-01           
         70  traj.phases.ballistic_ascent.indep_states.states:gam_5        c    -1.111111E+19     3.787859E-01     9.888889E-01           
         71  traj.phases.ballistic_ascent.indep_states.states:gam_6        c    -1.111111E+19     3.742288E-01     9.888889E-01           
         72  traj.phases.ballistic_ascent.indep_states.states:gam_7        c    -1.111111E+19     3.634519E-01     9.888889E-01           
         73  traj.phases.ballistic_ascent.indep_states.states:gam_8        c    -1.111111E+19     3.477784E-01     9.888889E-01           
         74  traj.phases.ballistic_ascent.indep_states.states:gam_9        c    -1.111111E+19     3.426181E-01     9.888889E-01           
         75  traj.phases.ballistic_ascent.indep_states.states:gam_10       c    -1.111111E+19     3.304299E-01     9.888889E-01           
         76  traj.phases.ballistic_ascent.indep_states.states:gam_11       c    -1.111111E+19     3.127422E-01     9.888889E-01           
         77  traj.phases.ballistic_ascent.indep_states.states:gam_12       c    -1.111111E+19     3.069288E-01     9.888889E-01           
         78  traj.phases.ballistic_ascent.indep_states.states:gam_13       c    -1.111111E+19     2.932186E-01     9.888889E-01           
         79  traj.phases.ballistic_ascent.indep_states.states:gam_14       c    -1.111111E+19     2.733748E-01     9.888889E-01           
         80  traj.phases.ballistic_ascent.indep_states.states:gam_15       c    -1.111111E+19     2.668667E-01     9.888889E-01           
         81  traj.phases.ballistic_ascent.indep_states.states:gam_16       c    -1.111111E+19     2.515467E-01     9.888889E-01           
         82  traj.phases.ballistic_ascent.indep_states.states:gam_17       c    -1.111111E+19     2.294473E-01     9.888889E-01           
         83  traj.phases.ballistic_ascent.indep_states.states:gam_18       c    -1.111111E+19     2.222193E-01     9.888889E-01           
         84  traj.phases.ballistic_ascent.indep_states.states:gam_19       c    -1.111111E+19     2.052451E-01     9.888889E-01           
         85  traj.phases.ballistic_ascent.indep_states.states:gam_20       c    -1.111111E+19     1.808643E-01     9.888889E-01           
         86  traj.phases.ballistic_ascent.indep_states.states:gam_21       c    -1.111111E+19     1.729178E-01     9.888889E-01           
         87  traj.phases.ballistic_ascent.indep_states.states:gam_22       c    -1.111111E+19     1.543129E-01     9.888889E-01           
         88  traj.phases.ballistic_ascent.indep_states.states:gam_23       c    -1.111111E+19     1.277334E-01     9.888889E-01           
         89  traj.phases.ballistic_ascent.indep_states.states:gam_24       c    -1.111111E+19     1.191081E-01     9.888889E-01           
         90  traj.phases.ballistic_ascent.indep_states.states:gam_25       c    -1.111111E+19     9.898934E-02     9.888889E-01           
         91  traj.phases.ballistic_ascent.indep_states.states:gam_26       c    -1.111111E+19     7.043546E-02     9.888889E-01           
         92  traj.phases.ballistic_ascent.indep_states.states:gam_27       c    -1.111111E+19     6.121840E-02     9.888889E-01           
         93  traj.phases.ballistic_ascent.indep_states.states:gam_28       c    -1.111111E+19     3.981478E-02     9.888889E-01           
         94  traj.phases.ballistic_ascent.indep_states.states:gam_29       c    -1.111111E+19     9.670790E-03     9.888889E-01           
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        100  traj.phases.ballistic_ascent.indep_states.states:v_5          c    -1.000000E+21     3.426668E+01     1.000000E+21           
        101  traj.phases.ballistic_ascent.indep_states.states:v_6          c    -1.000000E+21     3.376218E+01     1.000000E+21           
        102  traj.phases.ballistic_ascent.indep_states.states:v_7          c    -1.000000E+21     3.265056E+01     1.000000E+21           
        103  traj.phases.ballistic_ascent.indep_states.states:v_8          c    -1.000000E+21     3.121066E+01     1.000000E+21           
        104  traj.phases.ballistic_ascent.indep_states.states:v_9          c    -1.000000E+21     3.077630E+01     1.000000E+21           
        105  traj.phases.ballistic_ascent.indep_states.states:v_10         c    -1.000000E+21     2.981848E+01     1.000000E+21           
        106  traj.phases.ballistic_ascent.indep_states.states:v_11         c    -1.000000E+21     2.857691E+01     1.000000E+21           
        107  traj.phases.ballistic_ascent.indep_states.states:v_12         c    -1.000000E+21     2.820235E+01     1.000000E+21           
        108  traj.phases.ballistic_ascent.indep_states.states:v_13         c    -1.000000E+21     2.737665E+01     1.000000E+21           
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        110  traj.phases.ballistic_ascent.indep_states.states:v_15         c    -1.000000E+21     2.598553E+01     1.000000E+21           
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        112  traj.phases.ballistic_ascent.indep_states.states:v_17         c    -1.000000E+21     2.436198E+01     1.000000E+21           
        113  traj.phases.ballistic_ascent.indep_states.states:v_18         c    -1.000000E+21     2.408734E+01     1.000000E+21           
        114  traj.phases.ballistic_ascent.indep_states.states:v_19         c    -1.000000E+21     2.348471E+01     1.000000E+21           
        115  traj.phases.ballistic_ascent.indep_states.states:v_20         c    -1.000000E+21     2.271186E+01     1.000000E+21           
        116  traj.phases.ballistic_ascent.indep_states.states:v_21         c    -1.000000E+21     2.248111E+01     1.000000E+21           
        117  traj.phases.ballistic_ascent.indep_states.states:v_22         c    -1.000000E+21     2.197736E+01     1.000000E+21           
        118  traj.phases.ballistic_ascent.indep_states.states:v_23         c    -1.000000E+21     2.133764E+01     1.000000E+21           
        119  traj.phases.ballistic_ascent.indep_states.states:v_24         c    -1.000000E+21     2.114831E+01     1.000000E+21           
        120  traj.phases.ballistic_ascent.indep_states.states:v_25         c    -1.000000E+21     2.073825E+01     1.000000E+21           
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        124  traj.phases.ballistic_ascent.indep_states.states:v_29         c    -1.000000E+21     1.936335E+01     1.000000E+21           
        125  traj.phases.ballistic_ascent.indep_states.states:v_30         c    -1.000000E+21     1.925142E+01     1.000000E+21           
        126  traj.descent.t_initial_0                                      c     5.000000E-01     2.041459E+00     1.000000E+02           
        127  traj.descent.t_duration_0                                     c     5.000000E-02     2.327821E-01     1.000000E+01           
        128  traj.phases.descent.indep_states.states:r_0                   c    -1.000000E+21     4.867492E+01     1.000000E+21           
        129  traj.phases.descent.indep_states.states:r_1                   c    -1.000000E+21     5.025371E+01     1.000000E+21           
        130  traj.phases.descent.indep_states.states:r_2                   c    -1.000000E+21     5.239256E+01     1.000000E+21           
        131  traj.phases.descent.indep_states.states:r_3                   c    -1.000000E+21     5.306019E+01     1.000000E+21           
        132  traj.phases.descent.indep_states.states:r_4                   c    -1.000000E+21     5.457254E+01     1.000000E+21           
        133  traj.phases.descent.indep_states.states:r_5                   c    -1.000000E+21     5.662246E+01     1.000000E+21           
        134  traj.phases.descent.indep_states.states:r_6                   c    -1.000000E+21     5.726254E+01     1.000000E+21           
        135  traj.phases.descent.indep_states.states:r_7                   c    -1.000000E+21     5.871277E+01     1.000000E+21           
        136  traj.phases.descent.indep_states.states:r_8                   c    -1.000000E+21     6.067895E+01     1.000000E+21           
        137  traj.phases.descent.indep_states.states:r_9                   c    -1.000000E+21     6.129295E+01     1.000000E+21           
        138  traj.phases.descent.indep_states.states:r_10                  c    -1.000000E+21     6.268413E+01     1.000000E+21           
        139  traj.phases.descent.indep_states.states:r_11                  c    -1.000000E+21     6.457019E+01     1.000000E+21           
        140  traj.phases.descent.indep_states.states:r_12                  c    -1.000000E+21     6.515912E+01     1.000000E+21           
        141  traj.phases.descent.indep_states.states:r_13                  c    -1.000000E+21     6.649335E+01     1.000000E+21           
        142  traj.phases.descent.indep_states.states:r_14                  c    -1.000000E+21     6.830175E+01     1.000000E+21           
        143  traj.phases.descent.indep_states.states:r_15                  c    -1.000000E+21     6.886630E+01     1.000000E+21           
        144  traj.phases.descent.indep_states.states:r_16                  c    -1.000000E+21     7.014499E+01     1.000000E+21           
        145  traj.phases.descent.indep_states.states:r_17                  c    -1.000000E+21     7.187738E+01     1.000000E+21           
        146  traj.phases.descent.indep_states.states:r_18                  c    -1.000000E+21     7.241799E+01     1.000000E+21           
        147  traj.phases.descent.indep_states.states:r_19                  c    -1.000000E+21     7.364210E+01     1.000000E+21           
        148  traj.phases.descent.indep_states.states:r_20                  c    -1.000000E+21     7.529959E+01     1.000000E+21           
        149  traj.phases.descent.indep_states.states:r_21                  c    -1.000000E+21     7.581660E+01     1.000000E+21           
        150  traj.phases.descent.indep_states.states:r_22                  c    -1.000000E+21     7.698681E+01     1.000000E+21           
        151  traj.phases.descent.indep_states.states:r_23                  c    -1.000000E+21     7.857028E+01     1.000000E+21           
        152  traj.phases.descent.indep_states.states:r_24                  c    -1.000000E+21     7.906394E+01     1.000000E+21           
        153  traj.phases.descent.indep_states.states:r_25                  c    -1.000000E+21     8.018083E+01     1.000000E+21           
        154  traj.phases.descent.indep_states.states:r_26                  c    -1.000000E+21     8.169107E+01     1.000000E+21           
        155  traj.phases.descent.indep_states.states:r_27                  c    -1.000000E+21     8.216164E+01     1.000000E+21           
        156  traj.phases.descent.indep_states.states:r_28                  c    -1.000000E+21     8.322581E+01     1.000000E+21           
        157  traj.phases.descent.indep_states.states:r_29                  c    -1.000000E+21     8.466369E+01     1.000000E+21           
        158  traj.phases.descent.indep_states.states:r_30                  c    -1.000000E+21     8.511145E+01     1.000000E+21           
        159  traj.phases.descent.indep_states.states:h_0                   c    -1.000000E+21     2.308634E+01     1.000000E+21           
        160  traj.phases.descent.indep_states.states:h_1                   c    -1.000000E+21     2.305302E+01     1.000000E+21           
        161  traj.phases.descent.indep_states.states:h_2                   c    -1.000000E+21     2.289894E+01     1.000000E+21           
        162  traj.phases.descent.indep_states.states:h_3                   c    -1.000000E+21     2.282443E+01     1.000000E+21           
        163  traj.phases.descent.indep_states.states:h_4                   c    -1.000000E+21     2.260781E+01     1.000000E+21           
        164  traj.phases.descent.indep_states.states:h_5                   c    -1.000000E+21     2.220523E+01     1.000000E+21           
        165  traj.phases.descent.indep_states.states:h_6                   c    -1.000000E+21     2.205310E+01     1.000000E+21           
        166  traj.phases.descent.indep_states.states:h_7                   c    -1.000000E+21     2.166060E+01     1.000000E+21           
        167  traj.phases.descent.indep_states.states:h_8                   c    -1.000000E+21     2.101948E+01     1.000000E+21           
        168  traj.phases.descent.indep_states.states:h_9                   c    -1.000000E+21     2.079285E+01     1.000000E+21           
        169  traj.phases.descent.indep_states.states:h_10                  c    -1.000000E+21     2.023152E+01     1.000000E+21           
        170  traj.phases.descent.indep_states.states:h_11                  c    -1.000000E+21     1.936154E+01     1.000000E+21           
        171  traj.phases.descent.indep_states.states:h_12                  c    -1.000000E+21     1.906346E+01     1.000000E+21           
        172  traj.phases.descent.indep_states.states:h_13                  c    -1.000000E+21     1.834033E+01     1.000000E+21           
        173  traj.phases.descent.indep_states.states:h_14                  c    -1.000000E+21     1.725126E+01     1.000000E+21           
        174  traj.phases.descent.indep_states.states:h_15                  c    -1.000000E+21     1.688485E+01     1.000000E+21           
        175  traj.phases.descent.indep_states.states:h_16                  c    -1.000000E+21     1.600712E+01     1.000000E+21           
        176  traj.phases.descent.indep_states.states:h_17                  c    -1.000000E+21     1.470904E+01     1.000000E+21           
        177  traj.phases.descent.indep_states.states:h_18                  c    -1.000000E+21     1.427754E+01     1.000000E+21           
        178  traj.phases.descent.indep_states.states:h_19                  c    -1.000000E+21     1.325268E+01     1.000000E+21           
        179  traj.phases.descent.indep_states.states:h_20                  c    -1.000000E+21     1.175609E+01     1.000000E+21           
        180  traj.phases.descent.indep_states.states:h_21                  c    -1.000000E+21     1.126286E+01     1.000000E+21           
        181  traj.phases.descent.indep_states.states:h_22                  c    -1.000000E+21     1.009866E+01     1.000000E+21           
        182  traj.phases.descent.indep_states.states:h_23                  c    -1.000000E+21     8.414477E+00     1.000000E+21           
        183  traj.phases.descent.indep_states.states:h_24                  c    -1.000000E+21     7.863012E+00     1.000000E+21           
        184  traj.phases.descent.indep_states.states:h_25                  c    -1.000000E+21     6.567552E+00     1.000000E+21           
        185  traj.phases.descent.indep_states.states:h_26                  c    -1.000000E+21     4.707031E+00     1.000000E+21           
        186  traj.phases.descent.indep_states.states:h_27                  c    -1.000000E+21     4.100925E+00     1.000000E+21           
        187  traj.phases.descent.indep_states.states:h_28                  c    -1.000000E+21     2.682463E+00     1.000000E+21           
        188  traj.phases.descent.indep_states.states:h_29                  c    -1.000000E+21     6.570981E-01     1.000000E+21           
        189  traj.phases.descent.indep_states.states:gam_0                 c    -1.000000E+21    -4.157073E-30     1.000000E+21           
        190  traj.phases.descent.indep_states.states:gam_1                 c    -1.000000E+21    -2.429701E+00     1.000000E+21           
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        192  traj.phases.descent.indep_states.states:gam_3                 c    -1.000000E+21    -6.910356E+00     1.000000E+21           
        193  traj.phases.descent.indep_states.states:gam_4                 c    -1.000000E+21    -9.396827E+00     1.000000E+21           
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        195  traj.phases.descent.indep_states.states:gam_6                 c    -1.000000E+21    -1.391041E+01     1.000000E+21           
        196  traj.phases.descent.indep_states.states:gam_7                 c    -1.000000E+21    -1.637595E+01     1.000000E+21           
        197  traj.phases.descent.indep_states.states:gam_8                 c    -1.000000E+21    -1.973435E+01     1.000000E+21           
        198  traj.phases.descent.indep_states.states:gam_9                 c    -1.000000E+21    -2.078346E+01     1.000000E+21           
        199  traj.phases.descent.indep_states.states:gam_10                c    -1.000000E+21    -2.315574E+01     1.000000E+21           
        200  traj.phases.descent.indep_states.states:gam_11                c    -1.000000E+21    -2.634973E+01     1.000000E+21           
        201  traj.phases.descent.indep_states.states:gam_12                c    -1.000000E+21    -2.733906E+01     1.000000E+21           
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        204  traj.phases.descent.indep_states.states:gam_15                c    -1.000000E+21    -3.343943E+01     1.000000E+21           
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        218  traj.phases.descent.indep_states.states:gam_29                c    -1.000000E+21    -5.546843E+01     1.000000E+21           
        219  traj.phases.descent.indep_states.states:gam_30                c    -1.000000E+21    -5.598681E+01     1.000000E+21           
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        224  traj.phases.descent.indep_states.states:v_4                   c    -1.000000E+21     1.840830E+01     1.000000E+21           
        225  traj.phases.descent.indep_states.states:v_5                   c    -1.000000E+21     1.824708E+01     1.000000E+21           
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        228  traj.phases.descent.indep_states.states:v_8                   c    -1.000000E+21     1.813124E+01     1.000000E+21           
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        230  traj.phases.descent.indep_states.states:v_10                  c    -1.000000E+21     1.817219E+01     1.000000E+21           
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        232  traj.phases.descent.indep_states.states:v_12                  c    -1.000000E+21     1.830905E+01     1.000000E+21           
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        234  traj.phases.descent.indep_states.states:v_14                  c    -1.000000E+21     1.861287E+01     1.000000E+21           
        235  traj.phases.descent.indep_states.states:v_15                  c    -1.000000E+21     1.868199E+01     1.000000E+21           
        236  traj.phases.descent.indep_states.states:v_16                  c    -1.000000E+21     1.885401E+01     1.000000E+21           
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        238  traj.phases.descent.indep_states.states:v_18                  c    -1.000000E+21     1.921000E+01     1.000000E+21           
        239  traj.phases.descent.indep_states.states:v_19                  c    -1.000000E+21     1.942649E+01     1.000000E+21           
        240  traj.phases.descent.indep_states.states:v_20                  c    -1.000000E+21     1.974502E+01     1.000000E+21           
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        242  traj.phases.descent.indep_states.states:v_22                  c    -1.000000E+21     2.009674E+01     1.000000E+21           
        243  traj.phases.descent.indep_states.states:v_23                  c    -1.000000E+21     2.044963E+01     1.000000E+21           
        244  traj.phases.descent.indep_states.states:v_24                  c    -1.000000E+21     2.056377E+01     1.000000E+21           
        245  traj.phases.descent.indep_states.states:v_25                  c    -1.000000E+21     2.082870E+01     1.000000E+21           
        246  traj.phases.descent.indep_states.states:v_26                  c    -1.000000E+21     2.120052E+01     1.000000E+21           
        247  traj.phases.descent.indep_states.states:v_27                  c    -1.000000E+21     2.131927E+01     1.000000E+21           
        248  traj.phases.descent.indep_states.states:v_28                  c    -1.000000E+21     2.159246E+01     1.000000E+21           
        249  traj.phases.descent.indep_states.states:v_29                  c    -1.000000E+21     2.197079E+01     1.000000E+21           
        250  traj.phases.descent.indep_states.states:v_30                  c    -1.000000E+21     2.209052E+01     1.000000E+21           
        251  traj.propelled_ascent.t_duration_0                            c     1.000000E-02     1.126018E+00     5.000000E+00           
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        255  traj.phases.propelled_ascent.indep_states.states:r_3          c    -1.000000E+19     1.344992E-05     1.000000E+19           
        256  traj.phases.propelled_ascent.indep_states.states:r_4          c    -1.000000E+19     2.392361E-05     1.000000E+19           
        257  traj.phases.propelled_ascent.indep_states.states:r_5          c    -1.000000E+19     2.785918E-05     1.000000E+19           
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        259  traj.phases.propelled_ascent.indep_states.states:r_7          c    -1.000000E+19     5.453721E-05     1.000000E+19           
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        263  traj.phases.propelled_ascent.indep_states.states:r_11         c    -1.000000E+19     1.052429E-04     1.000000E+19           
        264  traj.phases.propelled_ascent.indep_states.states:r_12         c    -1.000000E+19     1.241161E-04     1.000000E+19           
        265  traj.phases.propelled_ascent.indep_states.states:r_13         c    -1.000000E+19     1.526833E-04     1.000000E+19           
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        267  traj.phases.propelled_ascent.indep_states.states:r_15         c    -1.000000E+19     1.855322E-04     1.000000E+19           
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        330  traj.phases.propelled_ascent.indep_states.states:r_78         c    -1.000000E+19     4.243147E-03     1.000000E+19           
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        339  traj.phases.propelled_ascent.indep_states.states:r_87         c    -1.000000E+19     5.265814E-03     1.000000E+19           
        340  traj.phases.propelled_ascent.indep_states.states:r_88         c    -1.000000E+19     5.444121E-03     1.000000E+19           
        341  traj.phases.propelled_ascent.indep_states.states:r_89         c    -1.000000E+19     5.501228E-03     1.000000E+19           
        342  traj.phases.propelled_ascent.indep_states.states:r_90         c    -1.000000E+19     5.633222E-03     1.000000E+19           
        343  traj.phases.propelled_ascent.indep_states.states:r_91         c    -1.000000E+19     5.818166E-03     1.000000E+19           
        344  traj.phases.propelled_ascent.indep_states.states:r_92         c    -1.000000E+19     5.877384E-03     1.000000E+19           
        345  traj.phases.propelled_ascent.indep_states.states:r_93         c    -1.000000E+19     6.014235E-03     1.000000E+19           
        346  traj.phases.propelled_ascent.indep_states.states:r_94         c    -1.000000E+19     6.205928E-03     1.000000E+19           
        347  traj.phases.propelled_ascent.indep_states.states:r_95         c    -1.000000E+19     6.267294E-03     1.000000E+19           
        348  traj.phases.propelled_ascent.indep_states.states:r_96         c    -1.000000E+19     6.409087E-03     1.000000E+19           
        349  traj.phases.propelled_ascent.indep_states.states:r_97         c    -1.000000E+19     6.607652E-03     1.000000E+19           
        350  traj.phases.propelled_ascent.indep_states.states:r_98         c    -1.000000E+19     6.671207E-03     1.000000E+19           
        351  traj.phases.propelled_ascent.indep_states.states:r_99         c    -1.000000E+19     6.818035E-03     1.000000E+19           
        352  traj.phases.propelled_ascent.indep_states.states:r_100        c    -1.000000E+19     7.023605E-03     1.000000E+19           
        353  traj.phases.propelled_ascent.indep_states.states:r_101        c    -1.000000E+19     7.089392E-03     1.000000E+19           
        354  traj.phases.propelled_ascent.indep_states.states:r_102        c    -1.000000E+19     7.241357E-03     1.000000E+19           
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        356  traj.phases.propelled_ascent.indep_states.states:r_104        c    -1.000000E+19     7.522145E-03     1.000000E+19           
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        506  traj.phases.propelled_ascent.indep_states.states:h_104        c    -1.000000E+19     6.212849E-03     1.000000E+19           
        507  traj.phases.propelled_ascent.indep_states.states:h_105        c    -1.000000E+19     6.339471E-03     1.000000E+19           
        508  traj.phases.propelled_ascent.indep_states.states:h_106        c    -1.000000E+19     6.516585E-03     1.000000E+19           
        509  traj.phases.propelled_ascent.indep_states.states:h_107        c    -1.000000E+19     6.573225E-03     1.000000E+19           
        510  traj.phases.propelled_ascent.indep_states.states:h_108        c    -1.000000E+19     6.703992E-03     1.000000E+19           
        511  traj.phases.propelled_ascent.indep_states.states:h_109        c    -1.000000E+19     6.886883E-03     1.000000E+19           
        512  traj.phases.propelled_ascent.indep_states.states:h_110        c    -1.000000E+19     6.945366E-03     1.000000E+19           
        513  traj.phases.propelled_ascent.indep_states.states:h_111        c    -1.000000E+19     7.080379E-03     1.000000E+19           
        514  traj.phases.propelled_ascent.indep_states.states:h_112        c    -1.000000E+19     7.269191E-03     1.000000E+19           
        515  traj.phases.propelled_ascent.indep_states.states:h_113        c    -1.000000E+19     7.329564E-03     1.000000E+19           
        516  traj.phases.propelled_ascent.indep_states.states:h_114        c    -1.000000E+19     7.468934E-03     1.000000E+19           
        517  traj.phases.propelled_ascent.indep_states.states:h_115        c    -1.000000E+19     7.663827E-03     1.000000E+19           
        518  traj.phases.propelled_ascent.indep_states.states:h_116        c    -1.000000E+19     7.726142E-03     1.000000E+19           
        519  traj.phases.propelled_ascent.indep_states.states:h_117        c    -1.000000E+19     7.869990E-03     1.000000E+19           
        520  traj.phases.propelled_ascent.indep_states.states:h_118        c    -1.000000E+19     8.071139E-03     1.000000E+19           
        521  traj.phases.propelled_ascent.indep_states.states:h_119        c    -1.000000E+19     8.135452E-03     1.000000E+19           
        522  traj.phases.propelled_ascent.indep_states.states:h_120        c    -1.000000E+19     8.283914E-03     1.000000E+19           
        523  traj.phases.propelled_ascent.indep_states.states:h_121        c    -1.000000E+19     8.491511E-03     1.000000E+19           
        524  traj.phases.propelled_ascent.indep_states.states:h_122        c    -1.000000E+19     8.557887E-03     1.000000E+19           
        525  traj.phases.propelled_ascent.indep_states.states:h_123        c    -1.000000E+19     8.711110E-03     1.000000E+19           
        526  traj.phases.propelled_ascent.indep_states.states:h_124        c    -1.000000E+19     8.925369E-03     1.000000E+19           
        527  traj.phases.propelled_ascent.indep_states.states:h_125        c    -1.000000E+19     8.993876E-03     1.000000E+19           
        528  traj.phases.propelled_ascent.indep_states.states:h_126        c    -1.000000E+19     9.152024E-03     1.000000E+19           
        529  traj.phases.propelled_ascent.indep_states.states:h_127        c    -1.000000E+19     9.373183E-03     1.000000E+19           
        530  traj.phases.propelled_ascent.indep_states.states:h_128        c    -1.000000E+19     9.443900E-03     1.000000E+19           
        531  traj.phases.propelled_ascent.indep_states.states:h_129        c    -1.000000E+19     9.607156E-03     1.000000E+19           
        532  traj.phases.propelled_ascent.indep_states.states:h_130        c    -1.000000E+19     9.835477E-03     1.000000E+19           
        533  traj.phases.propelled_ascent.indep_states.states:h_131        c    -1.000000E+19     9.908490E-03     1.000000E+19           
        534  traj.phases.propelled_ascent.indep_states.states:h_132        c    -1.000000E+19     1.007706E-02     1.000000E+19           
        535  traj.phases.propelled_ascent.indep_states.states:h_133        c    -1.000000E+19     1.031284E-02     1.000000E+19           
        536  traj.phases.propelled_ascent.indep_states.states:h_134        c    -1.000000E+19     1.038824E-02     1.000000E+19           
        537  traj.phases.propelled_ascent.indep_states.states:h_135        c    -1.000000E+19     1.056235E-02     1.000000E+19           
        538  traj.phases.propelled_ascent.indep_states.states:h_136        c    -1.000000E+19     1.080591E-02     1.000000E+19           
        539  traj.phases.propelled_ascent.indep_states.states:h_137        c    -1.000000E+19     1.088382E-02     1.000000E+19           
        540  traj.phases.propelled_ascent.indep_states.states:h_138        c    -1.000000E+19     1.106372E-02     1.000000E+19           
        541  traj.phases.propelled_ascent.indep_states.states:h_139        c    -1.000000E+19     1.131545E-02     1.000000E+19           
        542  traj.phases.propelled_ascent.indep_states.states:h_140        c    -1.000000E+19     1.139598E-02     1.000000E+19           
        543  traj.phases.propelled_ascent.indep_states.states:h_141        c    -1.000000E+19     1.158197E-02     1.000000E+19           
        544  traj.phases.propelled_ascent.indep_states.states:h_142        c    -1.000000E+19     1.184228E-02     1.000000E+19           
        545  traj.phases.propelled_ascent.indep_states.states:h_143        c    -1.000000E+19     1.192558E-02     1.000000E+19           
        546  traj.phases.propelled_ascent.indep_states.states:h_144        c    -1.000000E+19     1.211799E-02     1.000000E+19           
        547  traj.phases.propelled_ascent.indep_states.states:h_145        c    -1.000000E+19     1.238737E-02     1.000000E+19           
        548  traj.phases.propelled_ascent.indep_states.states:h_146        c    -1.000000E+19     1.247359E-02     1.000000E+19           
        549  traj.phases.propelled_ascent.indep_states.states:h_147        c    -1.000000E+19     1.267280E-02     1.000000E+19           
        550  traj.phases.propelled_ascent.indep_states.states:h_148        c    -1.000000E+19     1.295181E-02     1.000000E+19           
        551  traj.phases.propelled_ascent.indep_states.states:h_149        c    -1.000000E+19     1.304114E-02     1.000000E+19           
        552  traj.phases.propelled_ascent.indep_states.states:gam_0        c     0.000000E+00     5.121320E-01     9.444444E-01           
        553  traj.phases.propelled_ascent.indep_states.states:gam_1        c     0.000000E+00     4.914616E-01     9.444444E-01           
        554  traj.phases.propelled_ascent.indep_states.states:gam_2        c     0.000000E+00     4.853061E-01     9.444444E-01           
        555  traj.phases.propelled_ascent.indep_states.states:gam_3        c     0.000000E+00     4.820600E-01     9.444444E-01           
        556  traj.phases.propelled_ascent.indep_states.states:gam_4        c     0.000000E+00     4.783200E-01     9.444444E-01           
        557  traj.phases.propelled_ascent.indep_states.states:gam_5        c     0.000000E+00     4.744231E-01     9.444444E-01           
        558  traj.phases.propelled_ascent.indep_states.states:gam_6        c     0.000000E+00     4.733635E-01     9.444444E-01           
        559  traj.phases.propelled_ascent.indep_states.states:gam_7        c     0.000000E+00     4.712170E-01     9.444444E-01           
        560  traj.phases.propelled_ascent.indep_states.states:gam_8        c     0.000000E+00     4.687007E-01     9.444444E-01           
        561  traj.phases.propelled_ascent.indep_states.states:gam_9        c     0.000000E+00     4.679839E-01     9.444444E-01           
        562  traj.phases.propelled_ascent.indep_states.states:gam_10       c     0.000000E+00     4.664661E-01     9.444444E-01           
        563  traj.phases.propelled_ascent.indep_states.states:gam_11       c     0.000000E+00     4.645995E-01     9.444444E-01           
        564  traj.phases.propelled_ascent.indep_states.states:gam_12       c     0.000000E+00     4.640535E-01     9.444444E-01           
        565  traj.phases.propelled_ascent.indep_states.states:gam_13       c     0.000000E+00     4.628741E-01     9.444444E-01           
        566  traj.phases.propelled_ascent.indep_states.states:gam_14       c     0.000000E+00     4.613853E-01     9.444444E-01           
        567  traj.phases.propelled_ascent.indep_states.states:gam_15       c     0.000000E+00     4.609426E-01     9.444444E-01           
        568  traj.phases.propelled_ascent.indep_states.states:gam_16       c     0.000000E+00     4.599753E-01     9.444444E-01           
        569  traj.phases.propelled_ascent.indep_states.states:gam_17       c     0.000000E+00     4.587339E-01     9.444444E-01           
        570  traj.phases.propelled_ascent.indep_states.states:gam_18       c     0.000000E+00     4.583608E-01     9.444444E-01           
        571  traj.phases.propelled_ascent.indep_states.states:gam_19       c     0.000000E+00     4.575392E-01     9.444444E-01           
        572  traj.phases.propelled_ascent.indep_states.states:gam_20       c     0.000000E+00     4.564726E-01     9.444444E-01           
        573  traj.phases.propelled_ascent.indep_states.states:gam_21       c     0.000000E+00     4.561497E-01     9.444444E-01           
        574  traj.phases.propelled_ascent.indep_states.states:gam_22       c     0.000000E+00     4.554344E-01     9.444444E-01           
        575  traj.phases.propelled_ascent.indep_states.states:gam_23       c     0.000000E+00     4.544982E-01     9.444444E-01           
        576  traj.phases.propelled_ascent.indep_states.states:gam_24       c     0.000000E+00     4.542131E-01     9.444444E-01           
        577  traj.phases.propelled_ascent.indep_states.states:gam_25       c     0.000000E+00     4.535790E-01     9.444444E-01           
        578  traj.phases.propelled_ascent.indep_states.states:gam_26       c     0.000000E+00     4.527439E-01     9.444444E-01           
        579  traj.phases.propelled_ascent.indep_states.states:gam_27       c     0.000000E+00     4.524885E-01     9.444444E-01           
        580  traj.phases.propelled_ascent.indep_states.states:gam_28       c     0.000000E+00     4.519186E-01     9.444444E-01           
        581  traj.phases.propelled_ascent.indep_states.states:gam_29       c     0.000000E+00     4.511642E-01     9.444444E-01           
        582  traj.phases.propelled_ascent.indep_states.states:gam_30       c     0.000000E+00     4.509327E-01     9.444444E-01           
        583  traj.phases.propelled_ascent.indep_states.states:gam_31       c     0.000000E+00     4.504148E-01     9.444444E-01           
        584  traj.phases.propelled_ascent.indep_states.states:gam_32       c     0.000000E+00     4.497265E-01     9.444444E-01           
        585  traj.phases.propelled_ascent.indep_states.states:gam_33       c     0.000000E+00     4.495146E-01     9.444444E-01           
        586  traj.phases.propelled_ascent.indep_states.states:gam_34       c     0.000000E+00     4.490398E-01     9.444444E-01           
        587  traj.phases.propelled_ascent.indep_states.states:gam_35       c     0.000000E+00     4.484067E-01     9.444444E-01           
        588  traj.phases.propelled_ascent.indep_states.states:gam_36       c     0.000000E+00     4.482113E-01     9.444444E-01           
        589  traj.phases.propelled_ascent.indep_states.states:gam_37       c     0.000000E+00     4.477727E-01     9.444444E-01           
        590  traj.phases.propelled_ascent.indep_states.states:gam_38       c     0.000000E+00     4.471864E-01     9.444444E-01           
        591  traj.phases.propelled_ascent.indep_states.states:gam_39       c     0.000000E+00     4.470051E-01     9.444444E-01           
        592  traj.phases.propelled_ascent.indep_states.states:gam_40       c     0.000000E+00     4.465976E-01     9.444444E-01           
        593  traj.phases.propelled_ascent.indep_states.states:gam_41       c     0.000000E+00     4.460514E-01     9.444444E-01           
        594  traj.phases.propelled_ascent.indep_states.states:gam_42       c     0.000000E+00     4.458823E-01     9.444444E-01           
        595  traj.phases.propelled_ascent.indep_states.states:gam_43       c     0.000000E+00     4.455016E-01     9.444444E-01           
        596  traj.phases.propelled_ascent.indep_states.states:gam_44       c     0.000000E+00     4.449904E-01     9.444444E-01           
        597  traj.phases.propelled_ascent.indep_states.states:gam_45       c     0.000000E+00     4.448319E-01     9.444444E-01           
        598  traj.phases.propelled_ascent.indep_states.states:gam_46       c     0.000000E+00     4.444747E-01     9.444444E-01           
        599  traj.phases.propelled_ascent.indep_states.states:gam_47       c     0.000000E+00     4.439943E-01     9.444444E-01           
        600  traj.phases.propelled_ascent.indep_states.states:gam_48       c     0.000000E+00     4.438452E-01     9.444444E-01           
        601  traj.phases.propelled_ascent.indep_states.states:gam_49       c     0.000000E+00     4.435087E-01     9.444444E-01           
        602  traj.phases.propelled_ascent.indep_states.states:gam_50       c     0.000000E+00     4.430555E-01     9.444444E-01           
        603  traj.phases.propelled_ascent.indep_states.states:gam_51       c     0.000000E+00     4.429147E-01     9.444444E-01           
        604  traj.phases.propelled_ascent.indep_states.states:gam_52       c     0.000000E+00     4.425967E-01     9.444444E-01           
        605  traj.phases.propelled_ascent.indep_states.states:gam_53       c     0.000000E+00     4.421679E-01     9.444444E-01           
        606  traj.phases.propelled_ascent.indep_states.states:gam_54       c     0.000000E+00     4.420345E-01     9.444444E-01           
        607  traj.phases.propelled_ascent.indep_states.states:gam_55       c     0.000000E+00     4.417330E-01     9.444444E-01           
        608  traj.phases.propelled_ascent.indep_states.states:gam_56       c     0.000000E+00     4.413261E-01     9.444444E-01           
        609  traj.phases.propelled_ascent.indep_states.states:gam_57       c     0.000000E+00     4.411994E-01     9.444444E-01           
        610  traj.phases.propelled_ascent.indep_states.states:gam_58       c     0.000000E+00     4.409130E-01     9.444444E-01           
        611  traj.phases.propelled_ascent.indep_states.states:gam_59       c     0.000000E+00     4.405259E-01     9.444444E-01           
        612  traj.phases.propelled_ascent.indep_states.states:gam_60       c     0.000000E+00     4.404053E-01     9.444444E-01           
        613  traj.phases.propelled_ascent.indep_states.states:gam_61       c     0.000000E+00     4.401325E-01     9.444444E-01           
        614  traj.phases.propelled_ascent.indep_states.states:gam_62       c     0.000000E+00     4.397635E-01     9.444444E-01           
        615  traj.phases.propelled_ascent.indep_states.states:gam_63       c     0.000000E+00     4.396485E-01     9.444444E-01           
        616  traj.phases.propelled_ascent.indep_states.states:gam_64       c     0.000000E+00     4.393881E-01     9.444444E-01           
        617  traj.phases.propelled_ascent.indep_states.states:gam_65       c     0.000000E+00     4.390356E-01     9.444444E-01           
        618  traj.phases.propelled_ascent.indep_states.states:gam_66       c     0.000000E+00     4.389257E-01     9.444444E-01           
        619  traj.phases.propelled_ascent.indep_states.states:gam_67       c     0.000000E+00     4.386767E-01     9.444444E-01           
        620  traj.phases.propelled_ascent.indep_states.states:gam_68       c     0.000000E+00     4.383394E-01     9.444444E-01           
        621  traj.phases.propelled_ascent.indep_states.states:gam_69       c     0.000000E+00     4.382341E-01     9.444444E-01           
        622  traj.phases.propelled_ascent.indep_states.states:gam_70       c     0.000000E+00     4.379957E-01     9.444444E-01           
        623  traj.phases.propelled_ascent.indep_states.states:gam_71       c     0.000000E+00     4.376725E-01     9.444444E-01           
        624  traj.phases.propelled_ascent.indep_states.states:gam_72       c     0.000000E+00     4.375715E-01     9.444444E-01           
        625  traj.phases.propelled_ascent.indep_states.states:gam_73       c     0.000000E+00     4.373428E-01     9.444444E-01           
        626  traj.phases.propelled_ascent.indep_states.states:gam_74       c     0.000000E+00     4.370326E-01     9.444444E-01           
        627  traj.phases.propelled_ascent.indep_states.states:gam_75       c     0.000000E+00     4.369357E-01     9.444444E-01           
        628  traj.phases.propelled_ascent.indep_states.states:gam_76       c     0.000000E+00     4.367160E-01     9.444444E-01           
        629  traj.phases.propelled_ascent.indep_states.states:gam_77       c     0.000000E+00     4.364180E-01     9.444444E-01           
        630  traj.phases.propelled_ascent.indep_states.states:gam_78       c     0.000000E+00     4.363248E-01     9.444444E-01           
        631  traj.phases.propelled_ascent.indep_states.states:gam_79       c     0.000000E+00     4.361136E-01     9.444444E-01           
        632  traj.phases.propelled_ascent.indep_states.states:gam_80       c     0.000000E+00     4.358268E-01     9.444444E-01           
        633  traj.phases.propelled_ascent.indep_states.states:gam_81       c     0.000000E+00     4.357372E-01     9.444444E-01           
        634  traj.phases.propelled_ascent.indep_states.states:gam_82       c     0.000000E+00     4.355339E-01     9.444444E-01           
        635  traj.phases.propelled_ascent.indep_states.states:gam_83       c     0.000000E+00     4.352577E-01     9.444444E-01           
        636  traj.phases.propelled_ascent.indep_states.states:gam_84       c     0.000000E+00     4.351714E-01     9.444444E-01           
        637  traj.phases.propelled_ascent.indep_states.states:gam_85       c     0.000000E+00     4.349755E-01     9.444444E-01           
        638  traj.phases.propelled_ascent.indep_states.states:gam_86       c     0.000000E+00     4.347093E-01     9.444444E-01           
        639  traj.phases.propelled_ascent.indep_states.states:gam_87       c     0.000000E+00     4.346260E-01     9.444444E-01           
        640  traj.phases.propelled_ascent.indep_states.states:gam_88       c     0.000000E+00     4.344371E-01     9.444444E-01           
        641  traj.phases.propelled_ascent.indep_states.states:gam_89       c     0.000000E+00     4.341804E-01     9.444444E-01           
        642  traj.phases.propelled_ascent.indep_states.states:gam_90       c     0.000000E+00     4.341000E-01     9.444444E-01           
        643  traj.phases.propelled_ascent.indep_states.states:gam_91       c     0.000000E+00     4.339177E-01     9.444444E-01           
        644  traj.phases.propelled_ascent.indep_states.states:gam_92       c     0.000000E+00     4.336698E-01     9.444444E-01           
        645  traj.phases.propelled_ascent.indep_states.states:gam_93       c     0.000000E+00     4.335922E-01     9.444444E-01           
        646  traj.phases.propelled_ascent.indep_states.states:gam_94       c     0.000000E+00     4.334162E-01     9.444444E-01           
        647  traj.phases.propelled_ascent.indep_states.states:gam_95       c     0.000000E+00     4.331767E-01     9.444444E-01           
        648  traj.phases.propelled_ascent.indep_states.states:gam_96       c     0.000000E+00     4.331018E-01     9.444444E-01           
        649  traj.phases.propelled_ascent.indep_states.states:gam_97       c     0.000000E+00     4.329316E-01     9.444444E-01           
        650  traj.phases.propelled_ascent.indep_states.states:gam_98       c     0.000000E+00     4.327002E-01     9.444444E-01           
        651  traj.phases.propelled_ascent.indep_states.states:gam_99       c     0.000000E+00     4.326277E-01     9.444444E-01           
        652  traj.phases.propelled_ascent.indep_states.states:gam_100      c     0.000000E+00     4.324632E-01     9.444444E-01           
        653  traj.phases.propelled_ascent.indep_states.states:gam_101      c     0.000000E+00     4.322394E-01     9.444444E-01           
        654  traj.phases.propelled_ascent.indep_states.states:gam_102      c     0.000000E+00     4.321693E-01     9.444444E-01           
        655  traj.phases.propelled_ascent.indep_states.states:gam_103      c     0.000000E+00     4.320102E-01     9.444444E-01           
        656  traj.phases.propelled_ascent.indep_states.states:gam_104      c     0.000000E+00     4.317936E-01     9.444444E-01           
        657  traj.phases.propelled_ascent.indep_states.states:gam_105      c     0.000000E+00     4.317258E-01     9.444444E-01           
        658  traj.phases.propelled_ascent.indep_states.states:gam_106      c     0.000000E+00     4.315718E-01     9.444444E-01           
        659  traj.phases.propelled_ascent.indep_states.states:gam_107      c     0.000000E+00     4.313622E-01     9.444444E-01           
        660  traj.phases.propelled_ascent.indep_states.states:gam_108      c     0.000000E+00     4.312966E-01     9.444444E-01           
        661  traj.phases.propelled_ascent.indep_states.states:gam_109      c     0.000000E+00     4.311475E-01     9.444444E-01           
        662  traj.phases.propelled_ascent.indep_states.states:gam_110      c     0.000000E+00     4.309446E-01     9.444444E-01           
        663  traj.phases.propelled_ascent.indep_states.states:gam_111      c     0.000000E+00     4.308811E-01     9.444444E-01           
        664  traj.phases.propelled_ascent.indep_states.states:gam_112      c     0.000000E+00     4.307367E-01     9.444444E-01           
        665  traj.phases.propelled_ascent.indep_states.states:gam_113      c     0.000000E+00     4.305402E-01     9.444444E-01           
        666  traj.phases.propelled_ascent.indep_states.states:gam_114      c     0.000000E+00     4.304787E-01     9.444444E-01           
        667  traj.phases.propelled_ascent.indep_states.states:gam_115      c     0.000000E+00     4.303389E-01     9.444444E-01           
        668  traj.phases.propelled_ascent.indep_states.states:gam_116      c     0.000000E+00     4.301486E-01     9.444444E-01           
        669  traj.phases.propelled_ascent.indep_states.states:gam_117      c     0.000000E+00     4.300890E-01     9.444444E-01           
        670  traj.phases.propelled_ascent.indep_states.states:gam_118      c     0.000000E+00     4.299536E-01     9.444444E-01           
        671  traj.phases.propelled_ascent.indep_states.states:gam_119      c     0.000000E+00     4.297693E-01     9.444444E-01           
        672  traj.phases.propelled_ascent.indep_states.states:gam_120      c     0.000000E+00     4.297115E-01     9.444444E-01           
        673  traj.phases.propelled_ascent.indep_states.states:gam_121      c     0.000000E+00     4.295804E-01     9.444444E-01           
        674  traj.phases.propelled_ascent.indep_states.states:gam_122      c     0.000000E+00     4.294018E-01     9.444444E-01           
        675  traj.phases.propelled_ascent.indep_states.states:gam_123      c     0.000000E+00     4.293459E-01     9.444444E-01           
        676  traj.phases.propelled_ascent.indep_states.states:gam_124      c     0.000000E+00     4.292188E-01     9.444444E-01           
        677  traj.phases.propelled_ascent.indep_states.states:gam_125      c     0.000000E+00     4.290459E-01     9.444444E-01           
        678  traj.phases.propelled_ascent.indep_states.states:gam_126      c     0.000000E+00     4.289917E-01     9.444444E-01           
        679  traj.phases.propelled_ascent.indep_states.states:gam_127      c     0.000000E+00     4.288686E-01     9.444444E-01           
        680  traj.phases.propelled_ascent.indep_states.states:gam_128      c     0.000000E+00     4.287011E-01     9.444444E-01           
        681  traj.phases.propelled_ascent.indep_states.states:gam_129      c     0.000000E+00     4.286486E-01     9.444444E-01           
        682  traj.phases.propelled_ascent.indep_states.states:gam_130      c     0.000000E+00     4.285294E-01     9.444444E-01           
        683  traj.phases.propelled_ascent.indep_states.states:gam_131      c     0.000000E+00     4.283672E-01     9.444444E-01           
        684  traj.phases.propelled_ascent.indep_states.states:gam_132      c     0.000000E+00     4.283164E-01     9.444444E-01           
        685  traj.phases.propelled_ascent.indep_states.states:gam_133      c     0.000000E+00     4.282010E-01     9.444444E-01           
        686  traj.phases.propelled_ascent.indep_states.states:gam_134      c     0.000000E+00     4.280439E-01     9.444444E-01           
        687  traj.phases.propelled_ascent.indep_states.states:gam_135      c     0.000000E+00     4.279947E-01     9.444444E-01           
        688  traj.phases.propelled_ascent.indep_states.states:gam_136      c     0.000000E+00     4.278830E-01     9.444444E-01           
        689  traj.phases.propelled_ascent.indep_states.states:gam_137      c     0.000000E+00     4.277310E-01     9.444444E-01           
        690  traj.phases.propelled_ascent.indep_states.states:gam_138      c     0.000000E+00     4.276834E-01     9.444444E-01           
        691  traj.phases.propelled_ascent.indep_states.states:gam_139      c     0.000000E+00     4.275754E-01     9.444444E-01           
        692  traj.phases.propelled_ascent.indep_states.states:gam_140      c     0.000000E+00     4.274283E-01     9.444444E-01           
        693  traj.phases.propelled_ascent.indep_states.states:gam_141      c     0.000000E+00     4.273823E-01     9.444444E-01           
        694  traj.phases.propelled_ascent.indep_states.states:gam_142      c     0.000000E+00     4.272777E-01     9.444444E-01           
        695  traj.phases.propelled_ascent.indep_states.states:gam_143      c     0.000000E+00     4.271356E-01     9.444444E-01           
        696  traj.phases.propelled_ascent.indep_states.states:gam_144      c     0.000000E+00     4.270911E-01     9.444444E-01           
        697  traj.phases.propelled_ascent.indep_states.states:gam_145      c     0.000000E+00     4.269901E-01     9.444444E-01           
        698  traj.phases.propelled_ascent.indep_states.states:gam_146      c     0.000000E+00     4.268527E-01     9.444444E-01           
        699  traj.phases.propelled_ascent.indep_states.states:gam_147      c     0.000000E+00     4.268097E-01     9.444444E-01           
        700  traj.phases.propelled_ascent.indep_states.states:gam_148      c     0.000000E+00     4.267122E-01     9.444444E-01           
        701  traj.phases.propelled_ascent.indep_states.states:gam_149      c     0.000000E+00     4.265796E-01     9.444444E-01           
        702  traj.phases.propelled_ascent.indep_states.states:gam_150      c     0.000000E+00     4.265381E-01     9.444444E-01           
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        801  traj.phases.propelled_ascent.indep_states.states:v_98         c     1.000000E-04     2.346258E-01     1.000000E+19           
        802  traj.phases.propelled_ascent.indep_states.states:v_99         c     1.000000E-04     2.374791E-01     1.000000E+19           
        803  traj.phases.propelled_ascent.indep_states.states:v_100        c     1.000000E-04     2.414495E-01     1.000000E+19           
        804  traj.phases.propelled_ascent.indep_states.states:v_101        c     1.000000E-04     2.427145E-01     1.000000E+19           
        805  traj.phases.propelled_ascent.indep_states.states:v_102        c     1.000000E-04     2.456268E-01     1.000000E+19           
        806  traj.phases.propelled_ascent.indep_states.states:v_103        c     1.000000E-04     2.496819E-01     1.000000E+19           
        807  traj.phases.propelled_ascent.indep_states.states:v_104        c     1.000000E-04     2.509744E-01     1.000000E+19           
        808  traj.phases.propelled_ascent.indep_states.states:v_105        c     1.000000E-04     2.539513E-01     1.000000E+19           
        809  traj.phases.propelled_ascent.indep_states.states:v_106        c     1.000000E-04     2.580990E-01     1.000000E+19           
        810  traj.phases.propelled_ascent.indep_states.states:v_107        c     1.000000E-04     2.594217E-01     1.000000E+19           
        811  traj.phases.propelled_ascent.indep_states.states:v_108        c     1.000000E-04     2.624693E-01     1.000000E+19           
        812  traj.phases.propelled_ascent.indep_states.states:v_109        c     1.000000E-04     2.667182E-01     1.000000E+19           
        813  traj.phases.propelled_ascent.indep_states.states:v_110        c     1.000000E-04     2.680740E-01     1.000000E+19           
        814  traj.phases.propelled_ascent.indep_states.states:v_111        c     1.000000E-04     2.711989E-01     1.000000E+19           
        815  traj.phases.propelled_ascent.indep_states.states:v_112        c     1.000000E-04     2.755588E-01     1.000000E+19           
        816  traj.phases.propelled_ascent.indep_states.states:v_113        c     1.000000E-04     2.769507E-01     1.000000E+19           
        817  traj.phases.propelled_ascent.indep_states.states:v_114        c     1.000000E-04     2.801605E-01     1.000000E+19           
        818  traj.phases.propelled_ascent.indep_states.states:v_115        c     1.000000E-04     2.846423E-01     1.000000E+19           
        819  traj.phases.propelled_ascent.indep_states.states:v_116        c     1.000000E-04     2.860740E-01     1.000000E+19           
        820  traj.phases.propelled_ascent.indep_states.states:v_117        c     1.000000E-04     2.893770E-01     1.000000E+19           
        821  traj.phases.propelled_ascent.indep_states.states:v_118        c     1.000000E-04     2.939927E-01     1.000000E+19           
        822  traj.phases.propelled_ascent.indep_states.states:v_119        c     1.000000E-04     2.954681E-01     1.000000E+19           
        823  traj.phases.propelled_ascent.indep_states.states:v_120        c     1.000000E-04     2.988738E-01     1.000000E+19           
        824  traj.phases.propelled_ascent.indep_states.states:v_121        c     1.000000E-04     3.036372E-01     1.000000E+19           
        825  traj.phases.propelled_ascent.indep_states.states:v_122        c     1.000000E-04     3.051608E-01     1.000000E+19           
        826  traj.phases.propelled_ascent.indep_states.states:v_123        c     1.000000E-04     3.086799E-01     1.000000E+19           
        827  traj.phases.propelled_ascent.indep_states.states:v_124        c     1.000000E-04     3.136066E-01     1.000000E+19           
        828  traj.phases.propelled_ascent.indep_states.states:v_125        c     1.000000E-04     3.151837E-01     1.000000E+19           
        829  traj.phases.propelled_ascent.indep_states.states:v_126        c     1.000000E-04     3.188283E-01     1.000000E+19           
        830  traj.phases.propelled_ascent.indep_states.states:v_127        c     1.000000E-04     3.239361E-01     1.000000E+19           
        831  traj.phases.propelled_ascent.indep_states.states:v_128        c     1.000000E-04     3.255725E-01     1.000000E+19           
        832  traj.phases.propelled_ascent.indep_states.states:v_129        c     1.000000E-04     3.293567E-01     1.000000E+19           
        833  traj.phases.propelled_ascent.indep_states.states:v_130        c     1.000000E-04     3.346663E-01     1.000000E+19           
        834  traj.phases.propelled_ascent.indep_states.states:v_131        c     1.000000E-04     3.363688E-01     1.000000E+19           
        835  traj.phases.propelled_ascent.indep_states.states:v_132        c     1.000000E-04     3.403089E-01     1.000000E+19           
        836  traj.phases.propelled_ascent.indep_states.states:v_133        c     1.000000E-04     3.458441E-01     1.000000E+19           
        837  traj.phases.propelled_ascent.indep_states.states:v_134        c     1.000000E-04     3.476207E-01     1.000000E+19           
        838  traj.phases.propelled_ascent.indep_states.states:v_135        c     1.000000E-04     3.517357E-01     1.000000E+19           
        839  traj.phases.propelled_ascent.indep_states.states:v_136        c     1.000000E-04     3.575246E-01     1.000000E+19           
        840  traj.phases.propelled_ascent.indep_states.states:v_137        c     1.000000E-04     3.593846E-01     1.000000E+19           
        841  traj.phases.propelled_ascent.indep_states.states:v_138        c     1.000000E-04     3.636968E-01     1.000000E+19           
        842  traj.phases.propelled_ascent.indep_states.states:v_139        c     1.000000E-04     3.697727E-01     1.000000E+19           
        843  traj.phases.propelled_ascent.indep_states.states:v_140        c     1.000000E-04     3.717274E-01     1.000000E+19           
        844  traj.phases.propelled_ascent.indep_states.states:v_141        c     1.000000E-04     3.762635E-01     1.000000E+19           
        845  traj.phases.propelled_ascent.indep_states.states:v_142        c     1.000000E-04     3.826661E-01     1.000000E+19           
        846  traj.phases.propelled_ascent.indep_states.states:v_143        c     1.000000E-04     3.847288E-01     1.000000E+19           
        847  traj.phases.propelled_ascent.indep_states.states:v_144        c     1.000000E-04     3.895210E-01     1.000000E+19           
        848  traj.phases.propelled_ascent.indep_states.states:v_145        c     1.000000E-04     3.962985E-01     1.000000E+19           
        849  traj.phases.propelled_ascent.indep_states.states:v_146        c     1.000000E-04     3.984855E-01     1.000000E+19           
        850  traj.phases.propelled_ascent.indep_states.states:v_147        c     1.000000E-04     4.035730E-01     1.000000E+19           
        851  traj.phases.propelled_ascent.indep_states.states:v_148        c     1.000000E-04     4.107848E-01     1.000000E+19           
        852  traj.phases.propelled_ascent.indep_states.states:v_149        c     1.000000E-04     4.131161E-01     1.000000E+19           
        853  traj.phases.propelled_ascent.indep_states.states:p_0          c     1.020000E+00     6.420517E+00     1.000000E+21           
        854  traj.phases.propelled_ascent.indep_states.states:p_1          c     1.020000E+00     6.314633E+00     1.000000E+21           
        855  traj.phases.propelled_ascent.indep_states.states:p_2          c     1.020000E+00     6.281996E+00     1.000000E+21           
        856  traj.phases.propelled_ascent.indep_states.states:p_3          c     1.020000E+00     6.208781E+00     1.000000E+21           
        857  traj.phases.propelled_ascent.indep_states.states:p_4          c     1.020000E+00     6.111091E+00     1.000000E+21           
        858  traj.phases.propelled_ascent.indep_states.states:p_5          c     1.020000E+00     6.080944E+00     1.000000E+21           
        859  traj.phases.propelled_ascent.indep_states.states:p_6          c     1.020000E+00     6.013254E+00     1.000000E+21           
        860  traj.phases.propelled_ascent.indep_states.states:p_7          c     1.020000E+00     5.922805E+00     1.000000E+21           
        861  traj.phases.propelled_ascent.indep_states.states:p_8          c     1.020000E+00     5.894863E+00     1.000000E+21           
        862  traj.phases.propelled_ascent.indep_states.states:p_9          c     1.020000E+00     5.832071E+00     1.000000E+21           
        863  traj.phases.propelled_ascent.indep_states.states:p_10         c     1.020000E+00     5.748056E+00     1.000000E+21           
        864  traj.phases.propelled_ascent.indep_states.states:p_11         c     1.020000E+00     5.722075E+00     1.000000E+21           
        865  traj.phases.propelled_ascent.indep_states.states:p_12         c     1.020000E+00     5.663647E+00     1.000000E+21           
        866  traj.phases.propelled_ascent.indep_states.states:p_13         c     1.020000E+00     5.585376E+00     1.000000E+21           
        867  traj.phases.propelled_ascent.indep_states.states:p_14         c     1.020000E+00     5.561149E+00     1.000000E+21           
        868  traj.phases.propelled_ascent.indep_states.states:p_15         c     1.020000E+00     5.506628E+00     1.000000E+21           
        869  traj.phases.propelled_ascent.indep_states.states:p_16         c     1.020000E+00     5.433507E+00     1.000000E+21           
        870  traj.phases.propelled_ascent.indep_states.states:p_17         c     1.020000E+00     5.410856E+00     1.000000E+21           
        871  traj.phases.propelled_ascent.indep_states.states:p_18         c     1.020000E+00     5.359847E+00     1.000000E+21           
        872  traj.phases.propelled_ascent.indep_states.states:p_19         c     1.020000E+00     5.291365E+00     1.000000E+21           
        873  traj.phases.propelled_ascent.indep_states.states:p_20         c     1.020000E+00     5.270134E+00     1.000000E+21           
        874  traj.phases.propelled_ascent.indep_states.states:p_21         c     1.020000E+00     5.222294E+00     1.000000E+21           
        875  traj.phases.propelled_ascent.indep_states.states:p_22         c     1.020000E+00     5.158005E+00     1.000000E+21           
        876  traj.phases.propelled_ascent.indep_states.states:p_23         c     1.020000E+00     5.138060E+00     1.000000E+21           
        877  traj.phases.propelled_ascent.indep_states.states:p_24         c     1.020000E+00     5.093092E+00     1.000000E+21           
        878  traj.phases.propelled_ascent.indep_states.states:p_25         c     1.020000E+00     5.032608E+00     1.000000E+21           
        879  traj.phases.propelled_ascent.indep_states.states:p_26         c     1.020000E+00     5.013830E+00     1.000000E+21           
        880  traj.phases.propelled_ascent.indep_states.states:p_27         c     1.020000E+00     4.971473E+00     1.000000E+21           
        881  traj.phases.propelled_ascent.indep_states.states:p_28         c     1.020000E+00     4.914451E+00     1.000000E+21           
        882  traj.phases.propelled_ascent.indep_states.states:p_29         c     1.020000E+00     4.896737E+00     1.000000E+21           
        883  traj.phases.propelled_ascent.indep_states.states:p_30         c     1.020000E+00     4.856760E+00     1.000000E+21           
        884  traj.phases.propelled_ascent.indep_states.states:p_31         c     1.020000E+00     4.802900E+00     1.000000E+21           
        885  traj.phases.propelled_ascent.indep_states.states:p_32         c     1.020000E+00     4.786159E+00     1.000000E+21           
        886  traj.phases.propelled_ascent.indep_states.states:p_33         c     1.020000E+00     4.748359E+00     1.000000E+21           
        887  traj.phases.propelled_ascent.indep_states.states:p_34         c     1.020000E+00     4.697395E+00     1.000000E+21           
        888  traj.phases.propelled_ascent.indep_states.states:p_35         c     1.020000E+00     4.681545E+00     1.000000E+21           
        889  traj.phases.propelled_ascent.indep_states.states:p_36         c     1.020000E+00     4.645743E+00     1.000000E+21           
        890  traj.phases.propelled_ascent.indep_states.states:p_37         c     1.020000E+00     4.597438E+00     1.000000E+21           
        891  traj.phases.propelled_ascent.indep_states.states:p_38         c     1.020000E+00     4.582407E+00     1.000000E+21           
        892  traj.phases.propelled_ascent.indep_states.states:p_39         c     1.020000E+00     4.548441E+00     1.000000E+21           
        893  traj.phases.propelled_ascent.indep_states.states:p_40         c     1.020000E+00     4.502584E+00     1.000000E+21           
        894  traj.phases.propelled_ascent.indep_states.states:p_41         c     1.020000E+00     4.488307E+00     1.000000E+21           
        895  traj.phases.propelled_ascent.indep_states.states:p_42         c     1.020000E+00     4.456034E+00     1.000000E+21           
        896  traj.phases.propelled_ascent.indep_states.states:p_43         c     1.020000E+00     4.412436E+00     1.000000E+21           
        897  traj.phases.propelled_ascent.indep_states.states:p_44         c     1.020000E+00     4.398857E+00     1.000000E+21           
        898  traj.phases.propelled_ascent.indep_states.states:p_45         c     1.020000E+00     4.368149E+00     1.000000E+21           
        899  traj.phases.propelled_ascent.indep_states.states:p_46         c     1.020000E+00     4.326641E+00     1.000000E+21           
        900  traj.phases.propelled_ascent.indep_states.states:p_47         c     1.020000E+00     4.313706E+00     1.000000E+21           
        901  traj.phases.propelled_ascent.indep_states.states:p_48         c     1.020000E+00     4.284447E+00     1.000000E+21           
        902  traj.phases.propelled_ascent.indep_states.states:p_49         c     1.020000E+00     4.244876E+00     1.000000E+21           
        903  traj.phases.propelled_ascent.indep_states.states:p_50         c     1.020000E+00     4.232540E+00     1.000000E+21           
        904  traj.phases.propelled_ascent.indep_states.states:p_51         c     1.020000E+00     4.204626E+00     1.000000E+21           
        905  traj.phases.propelled_ascent.indep_states.states:p_52         c     1.020000E+00     4.166853E+00     1.000000E+21           
        906  traj.phases.propelled_ascent.indep_states.states:p_53         c     1.020000E+00     4.155074E+00     1.000000E+21           
        907  traj.phases.propelled_ascent.indep_states.states:p_54         c     1.020000E+00     4.128410E+00     1.000000E+21           
        908  traj.phases.propelled_ascent.indep_states.states:p_55         c     1.020000E+00     4.092312E+00     1.000000E+21           
        909  traj.phases.propelled_ascent.indep_states.states:p_56         c     1.020000E+00     4.081050E+00     1.000000E+21           
        910  traj.phases.propelled_ascent.indep_states.states:p_57         c     1.020000E+00     4.055552E+00     1.000000E+21           
        911  traj.phases.propelled_ascent.indep_states.states:p_58         c     1.020000E+00     4.021015E+00     1.000000E+21           
        912  traj.phases.propelled_ascent.indep_states.states:p_59         c     1.020000E+00     4.010236E+00     1.000000E+21           
        913  traj.phases.propelled_ascent.indep_states.states:p_60         c     1.020000E+00     3.985825E+00     1.000000E+21           
        914  traj.phases.propelled_ascent.indep_states.states:p_61         c     1.020000E+00     3.952745E+00     1.000000E+21           
        915  traj.phases.propelled_ascent.indep_states.states:p_62         c     1.020000E+00     3.942419E+00     1.000000E+21           
        916  traj.phases.propelled_ascent.indep_states.states:p_63         c     1.020000E+00     3.919024E+00     1.000000E+21           
        917  traj.phases.propelled_ascent.indep_states.states:p_64         c     1.020000E+00     3.887308E+00     1.000000E+21           
        918  traj.phases.propelled_ascent.indep_states.states:p_65         c     1.020000E+00     3.877404E+00     1.000000E+21           
        919  traj.phases.propelled_ascent.indep_states.states:p_66         c     1.020000E+00     3.854961E+00     1.000000E+21           
        920  traj.phases.propelled_ascent.indep_states.states:p_67         c     1.020000E+00     3.824523E+00     1.000000E+21           
        921  traj.phases.propelled_ascent.indep_states.states:p_68         c     1.020000E+00     3.815015E+00     1.000000E+21           
        922  traj.phases.propelled_ascent.indep_states.states:p_69         c     1.020000E+00     3.793465E+00     1.000000E+21           
        923  traj.phases.propelled_ascent.indep_states.states:p_70         c     1.020000E+00     3.764227E+00     1.000000E+21           
        924  traj.phases.propelled_ascent.indep_states.states:p_71         c     1.020000E+00     3.755091E+00     1.000000E+21           
        925  traj.phases.propelled_ascent.indep_states.states:p_72         c     1.020000E+00     3.734378E+00     1.000000E+21           
        926  traj.phases.propelled_ascent.indep_states.states:p_73         c     1.020000E+00     3.706267E+00     1.000000E+21           
        927  traj.phases.propelled_ascent.indep_states.states:p_74         c     1.020000E+00     3.697481E+00     1.000000E+21           
        928  traj.phases.propelled_ascent.indep_states.states:p_75         c     1.020000E+00     3.677557E+00     1.000000E+21           
        929  traj.phases.propelled_ascent.indep_states.states:p_76         c     1.020000E+00     3.650506E+00     1.000000E+21           
        930  traj.phases.propelled_ascent.indep_states.states:p_77         c     1.020000E+00     3.642049E+00     1.000000E+21           
        931  traj.phases.propelled_ascent.indep_states.states:p_78         c     1.020000E+00     3.622868E+00     1.000000E+21           
        932  traj.phases.propelled_ascent.indep_states.states:p_79         c     1.020000E+00     3.596817E+00     1.000000E+21           
        933  traj.phases.propelled_ascent.indep_states.states:p_80         c     1.020000E+00     3.588670E+00     1.000000E+21           
        934  traj.phases.propelled_ascent.indep_states.states:p_81         c     1.020000E+00     3.570189E+00     1.000000E+21           
        935  traj.phases.propelled_ascent.indep_states.states:p_82         c     1.020000E+00     3.545080E+00     1.000000E+21           
        936  traj.phases.propelled_ascent.indep_states.states:p_83         c     1.020000E+00     3.537226E+00     1.000000E+21           
        937  traj.phases.propelled_ascent.indep_states.states:p_84         c     1.020000E+00     3.519406E+00     1.000000E+21           
        938  traj.phases.propelled_ascent.indep_states.states:p_85         c     1.020000E+00     3.495189E+00     1.000000E+21           
        939  traj.phases.propelled_ascent.indep_states.states:p_86         c     1.020000E+00     3.487611E+00     1.000000E+21           
        940  traj.phases.propelled_ascent.indep_states.states:p_87         c     1.020000E+00     3.470416E+00     1.000000E+21           
        941  traj.phases.propelled_ascent.indep_states.states:p_88         c     1.020000E+00     3.447041E+00     1.000000E+21           
        942  traj.phases.propelled_ascent.indep_states.states:p_89         c     1.020000E+00     3.439725E+00     1.000000E+21           
        943  traj.phases.propelled_ascent.indep_states.states:p_90         c     1.020000E+00     3.423122E+00     1.000000E+21           
        944  traj.phases.propelled_ascent.indep_states.states:p_91         c     1.020000E+00     3.400543E+00     1.000000E+21           
        945  traj.phases.propelled_ascent.indep_states.states:p_92         c     1.020000E+00     3.393476E+00     1.000000E+21           
        946  traj.phases.propelled_ascent.indep_states.states:p_93         c     1.020000E+00     3.377433E+00     1.000000E+21           
        947  traj.phases.propelled_ascent.indep_states.states:p_94         c     1.020000E+00     3.355610E+00     1.000000E+21           
        948  traj.phases.propelled_ascent.indep_states.states:p_95         c     1.020000E+00     3.348778E+00     1.000000E+21           
        949  traj.phases.propelled_ascent.indep_states.states:p_96         c     1.020000E+00     3.333266E+00     1.000000E+21           
        950  traj.phases.propelled_ascent.indep_states.states:p_97         c     1.020000E+00     3.312160E+00     1.000000E+21           
        951  traj.phases.propelled_ascent.indep_states.states:p_98         c     1.020000E+00     3.305551E+00     1.000000E+21           
        952  traj.phases.propelled_ascent.indep_states.states:p_99         c     1.020000E+00     3.290543E+00     1.000000E+21           
        953  traj.phases.propelled_ascent.indep_states.states:p_100        c     1.020000E+00     3.270119E+00     1.000000E+21           
        954  traj.phases.propelled_ascent.indep_states.states:p_101        c     1.020000E+00     3.263722E+00     1.000000E+21           
        955  traj.phases.propelled_ascent.indep_states.states:p_102        c     1.020000E+00     3.249193E+00     1.000000E+21           
        956  traj.phases.propelled_ascent.indep_states.states:p_103        c     1.020000E+00     3.229416E+00     1.000000E+21           
        957  traj.phases.propelled_ascent.indep_states.states:p_104        c     1.020000E+00     3.223220E+00     1.000000E+21           
        958  traj.phases.propelled_ascent.indep_states.states:p_105        c     1.020000E+00     3.209147E+00     1.000000E+21           
        959  traj.phases.propelled_ascent.indep_states.states:p_106        c     1.020000E+00     3.189986E+00     1.000000E+21           
        960  traj.phases.propelled_ascent.indep_states.states:p_107        c     1.020000E+00     3.183982E+00     1.000000E+21           
        961  traj.phases.propelled_ascent.indep_states.states:p_108        c     1.020000E+00     3.170343E+00     1.000000E+21           
        962  traj.phases.propelled_ascent.indep_states.states:p_109        c     1.020000E+00     3.151768E+00     1.000000E+21           
        963  traj.phases.propelled_ascent.indep_states.states:p_110        c     1.020000E+00     3.145947E+00     1.000000E+21           
        964  traj.phases.propelled_ascent.indep_states.states:p_111        c     1.020000E+00     3.132721E+00     1.000000E+21           
        965  traj.phases.propelled_ascent.indep_states.states:p_112        c     1.020000E+00     3.114705E+00     1.000000E+21           
        966  traj.phases.propelled_ascent.indep_states.states:p_113        c     1.020000E+00     3.109058E+00     1.000000E+21           
        967  traj.phases.propelled_ascent.indep_states.states:p_114        c     1.020000E+00     3.096227E+00     1.000000E+21           
        968  traj.phases.propelled_ascent.indep_states.states:p_115        c     1.020000E+00     3.078744E+00     1.000000E+21           
        969  traj.phases.propelled_ascent.indep_states.states:p_116        c     1.020000E+00     3.073263E+00     1.000000E+21           
        970  traj.phases.propelled_ascent.indep_states.states:p_117        c     1.020000E+00     3.060808E+00     1.000000E+21           
        971  traj.phases.propelled_ascent.indep_states.states:p_118        c     1.020000E+00     3.043834E+00     1.000000E+21           
        972  traj.phases.propelled_ascent.indep_states.states:p_119        c     1.020000E+00     3.038512E+00     1.000000E+21           
        973  traj.phases.propelled_ascent.indep_states.states:p_120        c     1.020000E+00     3.026416E+00     1.000000E+21           
        974  traj.phases.propelled_ascent.indep_states.states:p_121        c     1.020000E+00     3.009929E+00     1.000000E+21           
        975  traj.phases.propelled_ascent.indep_states.states:p_122        c     1.020000E+00     3.004759E+00     1.000000E+21           
        976  traj.phases.propelled_ascent.indep_states.states:p_123        c     1.020000E+00     2.993006E+00     1.000000E+21           
        977  traj.phases.propelled_ascent.indep_states.states:p_124        c     1.020000E+00     2.976983E+00     1.000000E+21           
        978  traj.phases.propelled_ascent.indep_states.states:p_125        c     1.020000E+00     2.971958E+00     1.000000E+21           
        979  traj.phases.propelled_ascent.indep_states.states:p_126        c     1.020000E+00     2.960534E+00     1.000000E+21           
        980  traj.phases.propelled_ascent.indep_states.states:p_127        c     1.020000E+00     2.944956E+00     1.000000E+21           
        981  traj.phases.propelled_ascent.indep_states.states:p_128        c     1.020000E+00     2.940070E+00     1.000000E+21           
        982  traj.phases.propelled_ascent.indep_states.states:p_129        c     1.020000E+00     2.928960E+00     1.000000E+21           
        983  traj.phases.propelled_ascent.indep_states.states:p_130        c     1.020000E+00     2.913808E+00     1.000000E+21           
        984  traj.phases.propelled_ascent.indep_states.states:p_131        c     1.020000E+00     2.909055E+00     1.000000E+21           
        985  traj.phases.propelled_ascent.indep_states.states:p_132        c     1.020000E+00     2.898246E+00     1.000000E+21           
        986  traj.phases.propelled_ascent.indep_states.states:p_133        c     1.020000E+00     2.883503E+00     1.000000E+21           
        987  traj.phases.propelled_ascent.indep_states.states:p_134        c     1.020000E+00     2.878877E+00     1.000000E+21           
        988  traj.phases.propelled_ascent.indep_states.states:p_135        c     1.020000E+00     2.868357E+00     1.000000E+21           
        989  traj.phases.propelled_ascent.indep_states.states:p_136        c     1.020000E+00     2.854004E+00     1.000000E+21           
        990  traj.phases.propelled_ascent.indep_states.states:p_137        c     1.020000E+00     2.849501E+00     1.000000E+21           
        991  traj.phases.propelled_ascent.indep_states.states:p_138        c     1.020000E+00     2.839258E+00     1.000000E+21           
        992  traj.phases.propelled_ascent.indep_states.states:p_139        c     1.020000E+00     2.825281E+00     1.000000E+21           
        993  traj.phases.propelled_ascent.indep_states.states:p_140        c     1.020000E+00     2.820894E+00     1.000000E+21           
        994  traj.phases.propelled_ascent.indep_states.states:p_141        c     1.020000E+00     2.810917E+00     1.000000E+21           
        995  traj.phases.propelled_ascent.indep_states.states:p_142        c     1.020000E+00     2.797300E+00     1.000000E+21           
        996  traj.phases.propelled_ascent.indep_states.states:p_143        c     1.020000E+00     2.793026E+00     1.000000E+21           
        997  traj.phases.propelled_ascent.indep_states.states:p_144        c     1.020000E+00     2.783304E+00     1.000000E+21           
        998  traj.phases.propelled_ascent.indep_states.states:p_145        c     1.020000E+00     2.770033E+00     1.000000E+21           
        999  traj.phases.propelled_ascent.indep_states.states:p_146        c     1.020000E+00     2.765867E+00     1.000000E+21           
       1000  traj.phases.propelled_ascent.indep_states.states:p_147        c     1.020000E+00     2.756390E+00     1.000000E+21           
       1001  traj.phases.propelled_ascent.indep_states.states:p_148        c     1.020000E+00     2.743452E+00     1.000000E+21           
       1002  traj.phases.propelled_ascent.indep_states.states:p_149        c     1.020000E+00     2.739390E+00     1.000000E+21           
       1003  traj.phases.propelled_ascent.indep_states.states:V_w_0        c     0.000000E+00     1.026550E-01     1.000000E+20           
       1004  traj.phases.propelled_ascent.indep_states.states:V_w_1        c     0.000000E+00     1.016518E-01     1.000000E+20           
       1005  traj.phases.propelled_ascent.indep_states.states:V_w_2        c     0.000000E+00     1.002794E-01     1.000000E+20           
       1006  traj.phases.propelled_ascent.indep_states.states:V_w_3        c     0.000000E+00     9.984787E-02     1.000000E+20           
       1007  traj.phases.propelled_ascent.indep_states.states:V_w_4        c     0.000000E+00     9.886465E-02     1.000000E+20           
       1008  traj.phases.propelled_ascent.indep_states.states:V_w_5        c     0.000000E+00     9.751917E-02     1.000000E+20           
       1009  traj.phases.propelled_ascent.indep_states.states:V_w_6        c     0.000000E+00     9.709596E-02     1.000000E+20           
       1010  traj.phases.propelled_ascent.indep_states.states:V_w_7        c     0.000000E+00     9.613156E-02     1.000000E+20           
       1011  traj.phases.propelled_ascent.indep_states.states:V_w_8        c     0.000000E+00     9.481139E-02     1.000000E+20           
       1012  traj.phases.propelled_ascent.indep_states.states:V_w_9        c     0.000000E+00     9.439605E-02     1.000000E+20           
       1013  traj.phases.propelled_ascent.indep_states.states:V_w_10       c     0.000000E+00     9.344940E-02     1.000000E+20           
       1014  traj.phases.propelled_ascent.indep_states.states:V_w_11       c     0.000000E+00     9.215315E-02     1.000000E+20           
       1015  traj.phases.propelled_ascent.indep_states.states:V_w_12       c     0.000000E+00     9.174525E-02     1.000000E+20           
       1016  traj.phases.propelled_ascent.indep_states.states:V_w_13       c     0.000000E+00     9.081539E-02     1.000000E+20           
       1017  traj.phases.propelled_ascent.indep_states.states:V_w_14       c     0.000000E+00     8.954180E-02     1.000000E+20           
       1018  traj.phases.propelled_ascent.indep_states.states:V_w_15       c     0.000000E+00     8.914095E-02     1.000000E+20           
       1019  traj.phases.propelled_ascent.indep_states.states:V_w_16       c     0.000000E+00     8.822703E-02     1.000000E+20           
       1020  traj.phases.propelled_ascent.indep_states.states:V_w_17       c     0.000000E+00     8.697494E-02     1.000000E+20           
       1021  traj.phases.propelled_ascent.indep_states.states:V_w_18       c     0.000000E+00     8.658079E-02     1.000000E+20           
       1022  traj.phases.propelled_ascent.indep_states.states:V_w_19       c     0.000000E+00     8.568200E-02     1.000000E+20           
       1023  traj.phases.propelled_ascent.indep_states.states:V_w_20       c     0.000000E+00     8.445038E-02     1.000000E+20           
       1024  traj.phases.propelled_ascent.indep_states.states:V_w_21       c     0.000000E+00     8.406260E-02     1.000000E+20           
       1025  traj.phases.propelled_ascent.indep_states.states:V_w_22       c     0.000000E+00     8.317823E-02     1.000000E+20           
       1026  traj.phases.propelled_ascent.indep_states.states:V_w_23       c     0.000000E+00     8.196610E-02     1.000000E+20           
       1027  traj.phases.propelled_ascent.indep_states.states:V_w_24       c     0.000000E+00     8.158439E-02     1.000000E+20           
       1028  traj.phases.propelled_ascent.indep_states.states:V_w_25       c     0.000000E+00     8.071378E-02     1.000000E+20           
       1029  traj.phases.propelled_ascent.indep_states.states:V_w_26       c     0.000000E+00     7.952026E-02     1.000000E+20           
       1030  traj.phases.propelled_ascent.indep_states.states:V_w_27       c     0.000000E+00     7.914436E-02     1.000000E+20           
       1031  traj.phases.propelled_ascent.indep_states.states:V_w_28       c     0.000000E+00     7.828689E-02     1.000000E+20           
       1032  traj.phases.propelled_ascent.indep_states.states:V_w_29       c     0.000000E+00     7.711117E-02     1.000000E+20           
       1033  traj.phases.propelled_ascent.indep_states.states:V_w_30       c     0.000000E+00     7.674082E-02     1.000000E+20           
       1034  traj.phases.propelled_ascent.indep_states.states:V_w_31       c     0.000000E+00     7.589593E-02     1.000000E+20           
       1035  traj.phases.propelled_ascent.indep_states.states:V_w_32       c     0.000000E+00     7.473725E-02     1.000000E+20           
       1036  traj.phases.propelled_ascent.indep_states.states:V_w_33       c     0.000000E+00     7.437223E-02     1.000000E+20           
       1037  traj.phases.propelled_ascent.indep_states.states:V_w_34       c     0.000000E+00     7.353939E-02     1.000000E+20           
       1038  traj.phases.propelled_ascent.indep_states.states:V_w_35       c     0.000000E+00     7.239707E-02     1.000000E+20           
       1039  traj.phases.propelled_ascent.indep_states.states:V_w_36       c     0.000000E+00     7.203715E-02     1.000000E+20           
       1040  traj.phases.propelled_ascent.indep_states.states:V_w_37       c     0.000000E+00     7.121588E-02     1.000000E+20           
       1041  traj.phases.propelled_ascent.indep_states.states:V_w_38       c     0.000000E+00     7.008926E-02     1.000000E+20           
       1042  traj.phases.propelled_ascent.indep_states.states:V_w_39       c     0.000000E+00     6.973425E-02     1.000000E+20           
       1043  traj.phases.propelled_ascent.indep_states.states:V_w_40       c     0.000000E+00     6.892411E-02     1.000000E+20           
       1044  traj.phases.propelled_ascent.indep_states.states:V_w_41       c     0.000000E+00     6.781259E-02     1.000000E+20           
       1045  traj.phases.propelled_ascent.indep_states.states:V_w_42       c     0.000000E+00     6.746230E-02     1.000000E+20           
       1046  traj.phases.propelled_ascent.indep_states.states:V_w_43       c     0.000000E+00     6.666286E-02     1.000000E+20           
       1047  traj.phases.propelled_ascent.indep_states.states:V_w_44       c     0.000000E+00     6.556587E-02     1.000000E+20           
       1048  traj.phases.propelled_ascent.indep_states.states:V_w_45       c     0.000000E+00     6.522013E-02     1.000000E+20           
       1049  traj.phases.propelled_ascent.indep_states.states:V_w_46       c     0.000000E+00     6.443100E-02     1.000000E+20           
       1050  traj.phases.propelled_ascent.indep_states.states:V_w_47       c     0.000000E+00     6.334803E-02     1.000000E+20           
       1051  traj.phases.propelled_ascent.indep_states.states:V_w_48       c     0.000000E+00     6.300667E-02     1.000000E+20           
       1052  traj.phases.propelled_ascent.indep_states.states:V_w_49       c     0.000000E+00     6.222749E-02     1.000000E+20           
       1053  traj.phases.propelled_ascent.indep_states.states:V_w_50       c     0.000000E+00     6.115803E-02     1.000000E+20           
       1054  traj.phases.propelled_ascent.indep_states.states:V_w_51       c     0.000000E+00     6.082090E-02     1.000000E+20           
       1055  traj.phases.propelled_ascent.indep_states.states:V_w_52       c     0.000000E+00     6.005133E-02     1.000000E+20           
       1056  traj.phases.propelled_ascent.indep_states.states:V_w_53       c     0.000000E+00     5.899493E-02     1.000000E+20           
       1057  traj.phases.propelled_ascent.indep_states.states:V_w_54       c     0.000000E+00     5.866189E-02     1.000000E+20           
       1058  traj.phases.propelled_ascent.indep_states.states:V_w_55       c     0.000000E+00     5.790159E-02     1.000000E+20           
       1059  traj.phases.propelled_ascent.indep_states.states:V_w_56       c     0.000000E+00     5.685782E-02     1.000000E+20           
       1060  traj.phases.propelled_ascent.indep_states.states:V_w_57       c     0.000000E+00     5.652873E-02     1.000000E+20           
       1061  traj.phases.propelled_ascent.indep_states.states:V_w_58       c     0.000000E+00     5.577741E-02     1.000000E+20           
       1062  traj.phases.propelled_ascent.indep_states.states:V_w_59       c     0.000000E+00     5.474585E-02     1.000000E+20           
       1063  traj.phases.propelled_ascent.indep_states.states:V_w_60       c     0.000000E+00     5.442059E-02     1.000000E+20           
       1064  traj.phases.propelled_ascent.indep_states.states:V_w_61       c     0.000000E+00     5.367796E-02     1.000000E+20           
       1065  traj.phases.propelled_ascent.indep_states.states:V_w_62       c     0.000000E+00     5.265823E-02     1.000000E+20           
       1066  traj.phases.propelled_ascent.indep_states.states:V_w_63       c     0.000000E+00     5.233668E-02     1.000000E+20           
       1067  traj.phases.propelled_ascent.indep_states.states:V_w_64       c     0.000000E+00     5.160247E-02     1.000000E+20           
       1068  traj.phases.propelled_ascent.indep_states.states:V_w_65       c     0.000000E+00     5.059421E-02     1.000000E+20           
       1069  traj.phases.propelled_ascent.indep_states.states:V_w_66       c     0.000000E+00     5.027625E-02     1.000000E+20           
       1070  traj.phases.propelled_ascent.indep_states.states:V_w_67       c     0.000000E+00     4.955020E-02     1.000000E+20           
       1071  traj.phases.propelled_ascent.indep_states.states:V_w_68       c     0.000000E+00     4.855307E-02     1.000000E+20           
       1072  traj.phases.propelled_ascent.indep_states.states:V_w_69       c     0.000000E+00     4.823859E-02     1.000000E+20           
       1073  traj.phases.propelled_ascent.indep_states.states:V_w_70       c     0.000000E+00     4.752047E-02     1.000000E+20           
       1074  traj.phases.propelled_ascent.indep_states.states:V_w_71       c     0.000000E+00     4.653414E-02     1.000000E+20           
       1075  traj.phases.propelled_ascent.indep_states.states:V_w_72       c     0.000000E+00     4.622305E-02     1.000000E+20           
       1076  traj.phases.propelled_ascent.indep_states.states:V_w_73       c     0.000000E+00     4.551263E-02     1.000000E+20           
       1077  traj.phases.propelled_ascent.indep_states.states:V_w_74       c     0.000000E+00     4.453678E-02     1.000000E+20           
       1078  traj.phases.propelled_ascent.indep_states.states:V_w_75       c     0.000000E+00     4.422898E-02     1.000000E+20           
       1079  traj.phases.propelled_ascent.indep_states.states:V_w_76       c     0.000000E+00     4.352604E-02     1.000000E+20           
       1080  traj.phases.propelled_ascent.indep_states.states:V_w_77       c     0.000000E+00     4.256039E-02     1.000000E+20           
       1081  traj.phases.propelled_ascent.indep_states.states:V_w_78       c     0.000000E+00     4.225579E-02     1.000000E+20           
       1082  traj.phases.propelled_ascent.indep_states.states:V_w_79       c     0.000000E+00     4.156012E-02     1.000000E+20           
       1083  traj.phases.propelled_ascent.indep_states.states:V_w_80       c     0.000000E+00     4.060440E-02     1.000000E+20           
       1084  traj.phases.propelled_ascent.indep_states.states:V_w_81       c     0.000000E+00     4.030291E-02     1.000000E+20           
       1085  traj.phases.propelled_ascent.indep_states.states:V_w_82       c     0.000000E+00     3.961431E-02     1.000000E+20           
       1086  traj.phases.propelled_ascent.indep_states.states:V_w_83       c     0.000000E+00     3.866824E-02     1.000000E+20           
       1087  traj.phases.propelled_ascent.indep_states.states:V_w_84       c     0.000000E+00     3.836979E-02     1.000000E+20           
       1088  traj.phases.propelled_ascent.indep_states.states:V_w_85       c     0.000000E+00     3.768808E-02     1.000000E+20           
       1089  traj.phases.propelled_ascent.indep_states.states:V_w_86       c     0.000000E+00     3.675142E-02     1.000000E+20           
       1090  traj.phases.propelled_ascent.indep_states.states:V_w_87       c     0.000000E+00     3.645591E-02     1.000000E+20           
       1091  traj.phases.propelled_ascent.indep_states.states:V_w_88       c     0.000000E+00     3.578092E-02     1.000000E+20           
       1092  traj.phases.propelled_ascent.indep_states.states:V_w_89       c     0.000000E+00     3.485342E-02     1.000000E+20           
       1093  traj.phases.propelled_ascent.indep_states.states:V_w_90       c     0.000000E+00     3.456079E-02     1.000000E+20           
       1094  traj.phases.propelled_ascent.indep_states.states:V_w_91       c     0.000000E+00     3.389235E-02     1.000000E+20           
       1095  traj.phases.propelled_ascent.indep_states.states:V_w_92       c     0.000000E+00     3.297378E-02     1.000000E+20           
       1096  traj.phases.propelled_ascent.indep_states.states:V_w_93       c     0.000000E+00     3.268396E-02     1.000000E+20           
       1097  traj.phases.propelled_ascent.indep_states.states:V_w_94       c     0.000000E+00     3.202190E-02     1.000000E+20           
       1098  traj.phases.propelled_ascent.indep_states.states:V_w_95       c     0.000000E+00     3.111205E-02     1.000000E+20           
       1099  traj.phases.propelled_ascent.indep_states.states:V_w_96       c     0.000000E+00     3.082496E-02     1.000000E+20           
       1100  traj.phases.propelled_ascent.indep_states.states:V_w_97       c     0.000000E+00     3.016913E-02     1.000000E+20           
       1101  traj.phases.propelled_ascent.indep_states.states:V_w_98       c     0.000000E+00     2.926778E-02     1.000000E+20           
       1102  traj.phases.propelled_ascent.indep_states.states:V_w_99       c     0.000000E+00     2.898337E-02     1.000000E+20           
       1103  traj.phases.propelled_ascent.indep_states.states:V_w_100      c     0.000000E+00     2.833362E-02     1.000000E+20           
       1104  traj.phases.propelled_ascent.indep_states.states:V_w_101      c     0.000000E+00     2.744058E-02     1.000000E+20           
       1105  traj.phases.propelled_ascent.indep_states.states:V_w_102      c     0.000000E+00     2.715878E-02     1.000000E+20           
       1106  traj.phases.propelled_ascent.indep_states.states:V_w_103      c     0.000000E+00     2.651497E-02     1.000000E+20           
       1107  traj.phases.propelled_ascent.indep_states.states:V_w_104      c     0.000000E+00     2.563005E-02     1.000000E+20           
       1108  traj.phases.propelled_ascent.indep_states.states:V_w_105      c     0.000000E+00     2.535079E-02     1.000000E+20           
       1109  traj.phases.propelled_ascent.indep_states.states:V_w_106      c     0.000000E+00     2.471279E-02     1.000000E+20           
       1110  traj.phases.propelled_ascent.indep_states.states:V_w_107      c     0.000000E+00     2.383580E-02     1.000000E+20           
       1111  traj.phases.propelled_ascent.indep_states.states:V_w_108      c     0.000000E+00     2.355903E-02     1.000000E+20           
       1112  traj.phases.propelled_ascent.indep_states.states:V_w_109      c     0.000000E+00     2.292670E-02     1.000000E+20           
       1113  traj.phases.propelled_ascent.indep_states.states:V_w_110      c     0.000000E+00     2.205747E-02     1.000000E+20           
       1114  traj.phases.propelled_ascent.indep_states.states:V_w_111      c     0.000000E+00     2.178315E-02     1.000000E+20           
       1115  traj.phases.propelled_ascent.indep_states.states:V_w_112      c     0.000000E+00     2.115637E-02     1.000000E+20           
       1116  traj.phases.propelled_ascent.indep_states.states:V_w_113      c     0.000000E+00     2.029473E-02     1.000000E+20           
       1117  traj.phases.propelled_ascent.indep_states.states:V_w_114      c     0.000000E+00     2.002278E-02     1.000000E+20           
       1118  traj.phases.propelled_ascent.indep_states.states:V_w_115      c     0.000000E+00     1.940144E-02     1.000000E+20           
       1119  traj.phases.propelled_ascent.indep_states.states:V_w_116      c     0.000000E+00     1.854722E-02     1.000000E+20           
       1120  traj.phases.propelled_ascent.indep_states.states:V_w_117      c     0.000000E+00     1.827761E-02     1.000000E+20           
       1121  traj.phases.propelled_ascent.indep_states.states:V_w_118      c     0.000000E+00     1.766158E-02     1.000000E+20           
       1122  traj.phases.propelled_ascent.indep_states.states:V_w_119      c     0.000000E+00     1.681463E-02     1.000000E+20           
       1123  traj.phases.propelled_ascent.indep_states.states:V_w_120      c     0.000000E+00     1.654731E-02     1.000000E+20           
       1124  traj.phases.propelled_ascent.indep_states.states:V_w_121      c     0.000000E+00     1.593648E-02     1.000000E+20           
       1125  traj.phases.propelled_ascent.indep_states.states:V_w_122      c     0.000000E+00     1.509666E-02     1.000000E+20           
       1126  traj.phases.propelled_ascent.indep_states.states:V_w_123      c     0.000000E+00     1.483157E-02     1.000000E+20           
       1127  traj.phases.propelled_ascent.indep_states.states:V_w_124      c     0.000000E+00     1.422585E-02     1.000000E+20           
       1128  traj.phases.propelled_ascent.indep_states.states:V_w_125      c     0.000000E+00     1.339300E-02     1.000000E+20           
       1129  traj.phases.propelled_ascent.indep_states.states:V_w_126      c     0.000000E+00     1.313011E-02     1.000000E+20           
       1130  traj.phases.propelled_ascent.indep_states.states:V_w_127      c     0.000000E+00     1.252938E-02     1.000000E+20           
       1131  traj.phases.propelled_ascent.indep_states.states:V_w_128      c     0.000000E+00     1.170337E-02     1.000000E+20           
       1132  traj.phases.propelled_ascent.indep_states.states:V_w_129      c     0.000000E+00     1.144263E-02     1.000000E+20           
       1133  traj.phases.propelled_ascent.indep_states.states:V_w_130      c     0.000000E+00     1.084680E-02     1.000000E+20           
       1134  traj.phases.propelled_ascent.indep_states.states:V_w_131      c     0.000000E+00     1.002749E-02     1.000000E+20           
       1135  traj.phases.propelled_ascent.indep_states.states:V_w_132      c     0.000000E+00     9.768857E-03     1.000000E+20           
       1136  traj.phases.propelled_ascent.indep_states.states:V_w_133      c     0.000000E+00     9.177831E-03     1.000000E+20           
       1137  traj.phases.propelled_ascent.indep_states.states:V_w_134      c     0.000000E+00     8.365098E-03     1.000000E+20           
       1138  traj.phases.propelled_ascent.indep_states.states:V_w_135      c     0.000000E+00     8.108533E-03     1.000000E+20           
       1139  traj.phases.propelled_ascent.indep_states.states:V_w_136      c     0.000000E+00     7.522220E-03     1.000000E+20           
       1140  traj.phases.propelled_ascent.indep_states.states:V_w_137      c     0.000000E+00     6.715937E-03     1.000000E+20           
       1141  traj.phases.propelled_ascent.indep_states.states:V_w_138      c     0.000000E+00     6.461401E-03     1.000000E+20           
       1142  traj.phases.propelled_ascent.indep_states.states:V_w_139      c     0.000000E+00     5.879712E-03     1.000000E+20           
       1143  traj.phases.propelled_ascent.indep_states.states:V_w_140      c     0.000000E+00     5.079759E-03     1.000000E+20           
       1144  traj.phases.propelled_ascent.indep_states.states:V_w_141      c     0.000000E+00     4.827216E-03     1.000000E+20           
       1145  traj.phases.propelled_ascent.indep_states.states:V_w_142      c     0.000000E+00     4.250065E-03     1.000000E+20           
       1146  traj.phases.propelled_ascent.indep_states.states:V_w_143      c     0.000000E+00     3.456327E-03     1.000000E+20           
       1147  traj.phases.propelled_ascent.indep_states.states:V_w_144      c     0.000000E+00     3.205739E-03     1.000000E+20           
       1148  traj.phases.propelled_ascent.indep_states.states:V_w_145      c     0.000000E+00     2.633045E-03     1.000000E+20           
       1149  traj.phases.propelled_ascent.indep_states.states:V_w_146      c     0.000000E+00     1.845409E-03     1.000000E+20           
       1150  traj.phases.propelled_ascent.indep_states.states:V_w_147      c     0.000000E+00     1.596741E-03     1.000000E+20           
       1151  traj.phases.propelled_ascent.indep_states.states:V_w_148      c     0.000000E+00     1.028424E-03     1.000000E+20           
       1152  traj.phases.propelled_ascent.indep_states.states:V_w_149      c     0.000000E+00     2.467821E-04     1.000000E+20           

   Constraints (i - inequality, e - equality)
      Index  Name                                                                    Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
          0  traj.linkages.propelled_ascent:time_final|ballistic_ascent:time_initial    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          1  traj.linkages.propelled_ascent:r_final|ballistic_ascent:r_initial          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          2  traj.linkages.propelled_ascent:h_final|ballistic_ascent:h_initial          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          3  traj.linkages.propelled_ascent:gam_final|ballistic_ascent:gam_initial      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          4  traj.linkages.propelled_ascent:v_final|ballistic_ascent:v_initial          e   0.000000E+00   -7.105427E-15    0.000000E+00              9.00000E+100
          5  traj.linkages.ballistic_ascent:time_final|descent:time_initial             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          6  traj.linkages.ballistic_ascent:r_final|descent:r_initial                   e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          7  traj.linkages.ballistic_ascent:h_final|descent:h_initial                   e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          8  traj.linkages.ballistic_ascent:gam_final|descent:gam_initial               e   0.000000E+00    4.157073E-30    0.000000E+00              9.00000E+100
          9  traj.linkages.ballistic_ascent:v_final|descent:v_initial                   e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         10  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    4.111606E-15    0.000000E+00              9.00000E+100
         11  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00   -1.370535E-15    0.000000E+00              9.00000E+100
         12  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    2.055803E-15    0.000000E+00              9.00000E+100
         13  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00   -1.027901E-15    0.000000E+00              9.00000E+100
         14  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    3.083704E-15    0.000000E+00              9.00000E+100
         15  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    2.398437E-15    0.000000E+00              9.00000E+100
         16  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    8.565845E-15    0.000000E+00              9.00000E+100
         17  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    3.426338E-15    0.000000E+00              9.00000E+100
         18  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    7.195310E-15    0.000000E+00              9.00000E+100
         19  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    6.510043E-15    0.000000E+00              9.00000E+100
         20  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    8.565845E-15    0.000000E+00              9.00000E+100
         21  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    1.027901E-15    0.000000E+00              9.00000E+100
         22  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00   -2.398437E-15    0.000000E+00              9.00000E+100
         23  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    4.111606E-15    0.000000E+00              9.00000E+100
         24  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00   -5.139507E-15    0.000000E+00              9.00000E+100
         25  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00   -1.815959E-14    0.000000E+00              9.00000E+100
         26  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    3.426338E-15    0.000000E+00              9.00000E+100
         27  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00   -2.227120E-14    0.000000E+00              9.00000E+100
         28  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00   -3.152231E-14    0.000000E+00              9.00000E+100
         29  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00   -3.083704E-15    0.000000E+00              9.00000E+100
         30  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    1.233482E-14    0.000000E+00              9.00000E+100
         31  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    9.936381E-15    0.000000E+00              9.00000E+100
         32  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    7.537944E-15    0.000000E+00              9.00000E+100
         33  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    5.139507E-15    0.000000E+00              9.00000E+100
         34  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    1.027901E-15    0.000000E+00              9.00000E+100
         35  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00   -1.096428E-14    0.000000E+00              9.00000E+100
         36  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    1.336272E-14    0.000000E+00              9.00000E+100
         37  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    6.064619E-14    0.000000E+00              9.00000E+100
         38  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    6.852676E-15    0.000000E+00              9.00000E+100
         39  traj.phases.ballistic_ascent.collocation_constraint.defects:r              e   0.000000E+00    8.565845E-15    0.000000E+00              9.00000E+100
         40  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    4.796873E-15    0.000000E+00              9.00000E+100
         41  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    1.370535E-15    0.000000E+00              9.00000E+100
         42  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    2.055803E-15    0.000000E+00              9.00000E+100
         43  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -1.370535E-15    0.000000E+00              9.00000E+100
         44  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    1.713169E-15    0.000000E+00              9.00000E+100
         45  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    3.768972E-15    0.000000E+00              9.00000E+100
         46  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -3.083704E-15    0.000000E+00              9.00000E+100
         47  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    1.027901E-15    0.000000E+00              9.00000E+100
         48  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    3.083704E-15    0.000000E+00              9.00000E+100
         49  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -2.569754E-15    0.000000E+00              9.00000E+100
         50  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    2.227120E-15    0.000000E+00              9.00000E+100
         51  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -5.996092E-15    0.000000E+00              9.00000E+100
         52  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    7.366627E-15    0.000000E+00              9.00000E+100
         53  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -5.139507E-16    0.000000E+00              9.00000E+100
         54  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -1.199218E-15    0.000000E+00              9.00000E+100
         55  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    3.768972E-15    0.000000E+00              9.00000E+100
         56  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -3.255021E-15    0.000000E+00              9.00000E+100
         57  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -7.195310E-15    0.000000E+00              9.00000E+100
         58  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    4.111606E-15    0.000000E+00              9.00000E+100
         59  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    5.567800E-15    0.000000E+00              9.00000E+100
         60  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -6.852676E-16    0.000000E+00              9.00000E+100
         61  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    2.655412E-15    0.000000E+00              9.00000E+100
         62  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -2.826729E-15    0.000000E+00              9.00000E+100
         63  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    1.087862E-14    0.000000E+00              9.00000E+100
         64  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    5.524970E-15    0.000000E+00              9.00000E+100
         65  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    4.282923E-17    0.000000E+00              9.00000E+100
         66  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -5.011020E-15    0.000000E+00              9.00000E+100
         67  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -7.987651E-15    0.000000E+00              9.00000E+100
         68  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00    1.064306E-14    0.000000E+00              9.00000E+100
         69  traj.phases.ballistic_ascent.collocation_constraint.defects:h              e   0.000000E+00   -6.012153E-15    0.000000E+00              9.00000E+100
         70  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00    1.046937E-16    0.000000E+00              9.00000E+100
         71  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00   -1.675099E-16    0.000000E+00              9.00000E+100
         72  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00    1.751240E-16    0.000000E+00              9.00000E+100
         73  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00   -3.788007E-16    0.000000E+00              9.00000E+100
         74  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00    7.043029E-17    0.000000E+00              9.00000E+100
         75  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00   -2.170014E-16    0.000000E+00              9.00000E+100
         76  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00    5.006261E-16    0.000000E+00              9.00000E+100
         77  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00    4.187747E-17    0.000000E+00              9.00000E+100
         78  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00   -6.091268E-17    0.000000E+00              9.00000E+100
         79  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00   -7.043029E-17    0.000000E+00              9.00000E+100
         80  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00   -7.994789E-17    0.000000E+00              9.00000E+100
         81  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00    7.614085E-17    0.000000E+00              9.00000E+100
         82  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00    9.517606E-17    0.000000E+00              9.00000E+100
         83  traj.phases.ballistic_ascent.collocation_constraint.defects:gam            e   0.000000E+00   -3.807042E-18    0.000000E+00              9.00000E+100
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       1023  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    4.420465E-17    0.000000E+00              9.00000E+100
       1024  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.486156E-16    0.000000E+00              9.00000E+100
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       1026  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    5.200547E-18    0.000000E+00              9.00000E+100
       1027  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    3.420360E-17    0.000000E+00              9.00000E+100
       1028  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.200126E-17    0.000000E+00              9.00000E+100
       1029  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -2.560269E-17    0.000000E+00              9.00000E+100
       1030  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    9.200968E-18    0.000000E+00              9.00000E+100
       1031  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    3.160333E-17    0.000000E+00              9.00000E+100
       1032  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    4.000421E-18    0.000000E+00              9.00000E+100
       1033  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -3.680387E-17    0.000000E+00              9.00000E+100
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       1036  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    3.600379E-17    0.000000E+00              9.00000E+100
       1037  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -3.800400E-18    0.000000E+00              9.00000E+100
       1038  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.400147E-17    0.000000E+00              9.00000E+100
       1039  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -3.500368E-17    0.000000E+00              9.00000E+100
       1040  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.940204E-17    0.000000E+00              9.00000E+100
       1041  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    2.040215E-17    0.000000E+00              9.00000E+100
       1042  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -4.000421E-17    0.000000E+00              9.00000E+100
       1043  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.340141E-17    0.000000E+00              9.00000E+100
       1044  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.780187E-17    0.000000E+00              9.00000E+100
       1045  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.660175E-17    0.000000E+00              9.00000E+100
       1046  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -6.800716E-18    0.000000E+00              9.00000E+100
       1047  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    3.800400E-18    0.000000E+00              9.00000E+100
       1048  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -4.800505E-18    0.000000E+00              9.00000E+100
       1049  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -9.000947E-18    0.000000E+00              9.00000E+100
       1050  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -7.600800E-18    0.000000E+00              9.00000E+100
       1051  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.660175E-17    0.000000E+00              9.00000E+100
       1052  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    8.200863E-18    0.000000E+00              9.00000E+100
       1053  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.800189E-17    0.000000E+00              9.00000E+100
       1054  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    4.060427E-17    0.000000E+00              9.00000E+100
       1055  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    8.400884E-18    0.000000E+00              9.00000E+100
       1056  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -2.080219E-17    0.000000E+00              9.00000E+100
       1057  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -6.120644E-17    0.000000E+00              9.00000E+100
       1058  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    2.000211E-17    0.000000E+00              9.00000E+100
       1059  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -3.060322E-17    0.000000E+00              9.00000E+100
       1060  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    6.340667E-17    0.000000E+00              9.00000E+100
       1061  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -2.380251E-17    0.000000E+00              9.00000E+100
       1062  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    3.600379E-18    0.000000E+00              9.00000E+100
       1063  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.420149E-17    0.000000E+00              9.00000E+100
       1064  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    4.000421E-18    0.000000E+00              9.00000E+100
       1065  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    2.000211E-17    0.000000E+00              9.00000E+100
       1066  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    9.000947E-18    0.000000E+00              9.00000E+100
       1067  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.800189E-18    0.000000E+00              9.00000E+100
       1068  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.440152E-17    0.000000E+00              9.00000E+100
       1069  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    9.400989E-18    0.000000E+00              9.00000E+100
       1070  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    2.200232E-18    0.000000E+00              9.00000E+100
       1071  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.500158E-17    0.000000E+00              9.00000E+100
       1072  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -5.240552E-17    0.000000E+00              9.00000E+100
       1073  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.740183E-17    0.000000E+00              9.00000E+100
       1074  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    8.000842E-19    0.000000E+00              9.00000E+100
       1075  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    9.200968E-18    0.000000E+00              9.00000E+100
       1076  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
       1077  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -6.000632E-19    0.000000E+00              9.00000E+100
       1078  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.020107E-17    0.000000E+00              9.00000E+100
       1079  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    6.800716E-18    0.000000E+00              9.00000E+100
       1080  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -7.000737E-18    0.000000E+00              9.00000E+100
       1081  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    4.800505E-17    0.000000E+00              9.00000E+100
       1082  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -8.400884E-18    0.000000E+00              9.00000E+100
       1083  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    2.300242E-17    0.000000E+00              9.00000E+100
       1084  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -4.200442E-18    0.000000E+00              9.00000E+100
       1085  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.000105E-18    0.000000E+00              9.00000E+100
       1086  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    9.801032E-18    0.000000E+00              9.00000E+100
       1087  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -5.880619E-17    0.000000E+00              9.00000E+100
       1088  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -4.400463E-18    0.000000E+00              9.00000E+100
       1089  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    3.800400E-18    0.000000E+00              9.00000E+100
       1090  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -4.200442E-18    0.000000E+00              9.00000E+100
       1091  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    9.400989E-18    0.000000E+00              9.00000E+100
       1092  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -2.400253E-17    0.000000E+00              9.00000E+100
       1093  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    3.280345E-17    0.000000E+00              9.00000E+100
       1094  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.600168E-18    0.000000E+00              9.00000E+100
       1095  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    4.400463E-18    0.000000E+00              9.00000E+100
       1096  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -6.800716E-18    0.000000E+00              9.00000E+100
       1097  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.180124E-17    0.000000E+00              9.00000E+100
       1098  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -7.000737E-18    0.000000E+00              9.00000E+100
       1099  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -3.000316E-18    0.000000E+00              9.00000E+100
       1100  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    3.000316E-18    0.000000E+00              9.00000E+100
       1101  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -5.200547E-18    0.000000E+00              9.00000E+100
       1102  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.580166E-17    0.000000E+00              9.00000E+100
       1103  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -6.600695E-18    0.000000E+00              9.00000E+100
       1104  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
       1105  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.000105E-19    0.000000E+00              9.00000E+100
       1106  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    3.000316E-18    0.000000E+00              9.00000E+100
       1107  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -3.200337E-18    0.000000E+00              9.00000E+100
       1108  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    9.901042E-18    0.000000E+00              9.00000E+100
       1109  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -8.700916E-18    0.000000E+00              9.00000E+100
       1110  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    2.400253E-18    0.000000E+00              9.00000E+100
       1111  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.000105E-17    0.000000E+00              9.00000E+100
       1112  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -8.000842E-19    0.000000E+00              9.00000E+100
       1113  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.000105E-17    0.000000E+00              9.00000E+100
       1114  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.010106E-17    0.000000E+00              9.00000E+100
       1115  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.800189E-18    0.000000E+00              9.00000E+100
       1116  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -5.600589E-18    0.000000E+00              9.00000E+100
       1117  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.900200E-17    0.000000E+00              9.00000E+100
       1118  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.000105E-18    0.000000E+00              9.00000E+100
       1119  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -9.300979E-18    0.000000E+00              9.00000E+100
       1120  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.010106E-17    0.000000E+00              9.00000E+100
       1121  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.100116E-18    0.000000E+00              9.00000E+100
       1122  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    8.800926E-18    0.000000E+00              9.00000E+100
       1123  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -3.600379E-18    0.000000E+00              9.00000E+100
       1124  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -5.500579E-18    0.000000E+00              9.00000E+100
       1125  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    2.500263E-18    0.000000E+00              9.00000E+100
       1126  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    2.300242E-18    0.000000E+00              9.00000E+100
       1127  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -8.000842E-19    0.000000E+00              9.00000E+100
       1128  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    6.000632E-19    0.000000E+00              9.00000E+100
       1129  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -7.400779E-18    0.000000E+00              9.00000E+100
       1130  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    2.900305E-18    0.000000E+00              9.00000E+100
       1131  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.300137E-18    0.000000E+00              9.00000E+100
       1132  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    9.000947E-19    0.000000E+00              9.00000E+100
       1133  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.700179E-18    0.000000E+00              9.00000E+100
       1134  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -5.200547E-18    0.000000E+00              9.00000E+100
       1135  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    3.700389E-18    0.000000E+00              9.00000E+100
       1136  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.100116E-18    0.000000E+00              9.00000E+100
       1137  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.800189E-18    0.000000E+00              9.00000E+100
       1138  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -2.900305E-18    0.000000E+00              9.00000E+100
       1139  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    4.000421E-19    0.000000E+00              9.00000E+100
       1140  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -9.000947E-19    0.000000E+00              9.00000E+100
       1141  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.100116E-18    0.000000E+00              9.00000E+100
       1142  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    3.000316E-19    0.000000E+00              9.00000E+100
       1143  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.700179E-18    0.000000E+00              9.00000E+100
       1144  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    1.000105E-19    0.000000E+00              9.00000E+100
       1145  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    5.000526E-19    0.000000E+00              9.00000E+100
       1146  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -1.100116E-18    0.000000E+00              9.00000E+100
       1147  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00    6.000632E-19    0.000000E+00              9.00000E+100
       1148  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -3.000316E-19    0.000000E+00              9.00000E+100
       1149  traj.phases.propelled_ascent.collocation_constraint.defects:V_w            e   0.000000E+00   -2.000211E-19    0.000000E+00              9.00000E+100


   Exit Status
      Inform  Description
           0  Solve Succeeded
--------------------------------------------------------------------------------

/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/recorders/sqlite_recorder.py:227: UserWarning:The existing case recorder file, dymos_simulation.db, is being overwritten.

Simulating trajectory traj
Model viewer data has already been recorded for Driver.

Done simulating trajectory traj

Launch angle: 46.0919 deg
Flight angle at end of propulsion: 38.3884 deg
Empty mass: 0.1891 kg
Water volume: 1.0265 L
Maximum range: 85.1114 m
Maximum height: 23.0863 m
Maximum velocity: 41.3116 m/s

Maximum Range Solution: Propulsive Phase

plot_propelled_ascent(sol_out, sim_out)

Maximum Range Solution: Height vs. Range

plot_trajectory(sol_out, sim_out, legend_loc='center')

Maximum Range Solution: State History

plot_states(sol_out, sim_out, legend_loc='lower center')

References

[air13]

Nozzles. 2013. URL: http://www.aircommandrockets.com/nozzles.htm.

[BM20]

Bernardo Bahia Monteiro. Optimization of a water rocket in openmdao/dymos. Aug 2020. URL: engrxiv.org/nqta8, doi:10.31224/osf.io/nqta8.

[BPBMADiazFernandezO09]

R Barrio-Perotti, E Blanco-Marigorta, K Argüelles-D\'ıaz, and J Fernández-Oro. Experimental evaluation of the drag coefficient of water rockets by a simple free-fall test. European Journal of Physics, 30(5):1039–1048, jul 2009. doi:10.1088/0143-0807/30/5/012.

[FGH+20]

Laura Fischer, Thomas Günther, Linda Herzig, Tobias Jarzina, Frank Klinker, Sabine Knipper, Franz-Georg Schürmann, and Marvin Wollek. On the approximation of D.I.Y. water rocket dynamics including air drag. arXiv:2001.08828, 2020. arXiv:2001.08828.

[RBM13]

Alejandro Romanelli, Italo Bove, and Federico González Madina. Air expansion in a water rocket. American Journal of Physics, 81(10):762–766, oct 2013. doi:10.1119/1.4811116.

[TRP09]

Glen E. Thorncroft, John R. Ridgely, and Christopher C. Pascual. Hydrodynamics and thrust characteristics of a water-propelled rocket. International Journal of Mechanical Engineering Education, 37(3):241–261, jul 2009. doi:10.7227/ijmee.37.3.9.