# Single-Phase Space Shuttle Reentry#

The problem of the space shuttle reentering Earth’s atmosphere is an optimal control problem governed by six equations of motion and limited by the aerodynamic heating rate. For a detailed layout of this problem and other optimal control problems see Betts [Bet10]. The governing equations of motion for this problem are:

(74)#\begin{align} \frac{dh}{dt} &= v \sin \gamma \\ \frac{d\phi}{dt} &= \frac{v}{r} \cos \gamma \frac{\sin \psi}{\cos \theta} \\ \frac{d\theta}{dt} &= \frac{v}{r} \cos \gamma \cos \psi \\ \frac{dv}{dt} &= - \frac{D}{m} - g \sin \gamma \\ \frac{d\gamma}{dt} &= \frac{L}{mv} \cos \beta + \cos \gamma (\frac{v}{r} - \frac{g}{v}) \\ \frac{d\psi}{dt} &= \frac{L \sin \beta}{mv \cos \gamma} + \frac{v}{r \cos \theta} \cos \gamma \sin \psi \sin \theta \end{align}

where $$v$$ $$[ft/s]$$ is airspeed, $$\gamma$$ $$[rad]$$ is flight path angle, $$r$$ $$[ft]$$ is distance from the center of the Earth, $$\psi$$ $$[rad]$$ is azimuth, $$\theta$$ $$[rad]$$ is latitude, $$D$$ $$[lb]$$ is drag, $$m$$ $$[sl]$$ is mass, $$g$$ $$[\frac{ft}{s^2}]$$ is the local gravitational acceleration, $$L$$ $$[lb]$$ is lift, $$\beta$$ $$[rad]$$ is bank angle, $$h$$ $$[ft]$$ is altitude, and $$\phi$$ $$[rad]$$ is longitude. Mass is considered to be a constant for this case, because the model spans the time from when the shuttle begins reentry to the time right before the shuttle starts its engines. The engines are not actually running at any time during the model, so there is no thrust and thus no mass lost. The goal is to maximize the crossrange (latitude) that the shuttle can cover before reaching the final altitude, without exceding a maximum heat rate at the leading edges. This heat rate is constrained by $$q \leq 70$$ where q $$[\frac{btu}{ft^2s}]$$ is the heating rate.

The initial conditions are

(75)#\begin{align} h_0 &= 26000 \\ v_0 &= 25600 \\ \phi_0 &= 0 \\ \gamma_0 &= -0.01745 \\ \theta_0 &= 0 \\ \psi_0 &= \frac{\pi}{2} \end{align}

and the final conditions are

(76)#\begin{align} h_0 &= 80000 \\ v_0 &= 2500 \\ \gamma_0 &= -0.08727 \\ \theta &= \rm{free} \\ \psi &= \rm{free} \end{align}

Notice that no final condition appears for $$\phi$$. This is because none of the equations of motion actually depend on $$\phi$$, and as a result, while $$\phi$$ exists in the dymos model (last code block below) as a state variable, it does not exist as either an input or output in the ode (ShuttleODE group, second to last code block below).

This model uses four explicit OpenMDAO components. The first component computes the local atmospheric condition at the shuttle’s altitude. The second component computes the aerodynamic forces of lift and drag on the shuttle. The third component is where the heating rate on the leading edge of the shuttles wings is computed. The heating rate is given by $$q = q_a q_r$$ where

(77)#\begin{align} q_a &= c_0 + c_1\alpha + c_2 \alpha^2 + c_3 \alpha^3 \end{align}

and

(78)#\begin{align} q_r &= 17700 \rho^.5 (.0001v)^{3.07} \end{align}

where $$c_0, c_1, c_2,$$ and $$c_3$$ are constants, $$\alpha$$ $$[deg]$$ is the angle of attack, $$\rho$$ $$[\frac{sl}{ft^3}]$$ is local atmospheric density, and $$v$$ $$[\frac{ft}{s}]$$ is velocity. The final component is where the equations of motion are implemented. These four components are put together in the ShuttleODE group, which is the top level ode that the dymos model sees.

## Component Models#

Below is the code for the atmospheric component:

import numpy as np
import openmdao.api as om

class Atmosphere(om.ExplicitComponent):
"""
Defines the logarithmic atmosphere model for the shuttle reentry problem.

References
----------
.. [1] Betts, John T., Practical Methods for Optimal Control and Estimation Using Nonlinear
Programming, p. 248, 2010.
"""

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

def setup(self):
nn = self.options['num_nodes']
partial_range = np.arange(nn, dtype=int)
self.declare_partials('rho', 'h', rows=partial_range, cols=partial_range)

def compute(self, inputs, outputs):
h = inputs['h']
h_r = 23800
rho_0 = .002378
outputs['rho'] = rho_0 * np.exp(-h / h_r)

def compute_partials(self, inputs, partials):
h = inputs['h']
h_r = 23800
rho_0 = .002378
partials['rho', 'h'] = -1 / h_r * rho_0 * np.exp(-h / h_r)


Below is the code for the aerodynamics component:

import numpy as np
import openmdao.api as om

class Aerodynamics(om.ExplicitComponent):
"""
Defines the aerodynamics for the shuttle reentry problem.

References
----------
.. [1] Betts, John T., Practical Methods for Optimal Control and Estimation Using Nonlinear
Programming, p. 248, 2010.
"""

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

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

self.add_input('alpha', val=np.ones(nn), desc='angle of attack', units='deg')
self.add_input('v', val=np.ones(nn), desc='velocity of shuttle', units='ft/s')
units='slug/ft**3')

self.add_output('drag', val=np.ones(nn), desc='drag on shuttle', units='lb')
self.add_output('lift', val=np.ones(nn), desc='lift on shuttle', units='lb')

partial_range = np.arange(nn, dtype=int)

self.declare_partials('drag', 'alpha', rows=partial_range, cols=partial_range)
self.declare_partials('drag', 'v', rows=partial_range, cols=partial_range)
self.declare_partials('drag', 'rho', rows=partial_range, cols=partial_range)
self.declare_partials('lift', 'alpha', rows=partial_range, cols=partial_range)
self.declare_partials('lift', 'v', rows=partial_range, cols=partial_range)
self.declare_partials('lift', 'rho', rows=partial_range, cols=partial_range)

def compute(self, inputs, outputs):
a_0 = -.20704
a_1 = .029244
b_0 = .07854
b_1 = -.61592e-2
b_2 = .621408e-3
S = 2690
alpha = inputs['alpha']
v = inputs['v']
rho = inputs['rho']
c_L = a_0 + a_1 * alpha
c_D = b_0 + b_1 * alpha + b_2 * alpha ** 2

outputs['drag'] = .5 * c_D * S * rho * v ** 2
outputs['lift'] = .5 * c_L * S * rho * v ** 2

def compute_partials(self, inputs, J):
alpha = inputs['alpha']
v = inputs['v']
rho = inputs['rho']
a_0 = -.20704
a_1 = .029244
b_0 = .07854
b_1 = -.61592e-2
b_2 = .621408e-3
S = 2690
c_L = a_0 + a_1 * alpha
c_D = b_0 + b_1 * alpha + b_2 * alpha ** 2

dD_dCD = .5 * S * rho * v ** 2
dCD_dalpha = b_1 + 2 * alpha * b_2
dL_dCL = dD_dCD
dCL_dalpha = a_1

J['drag', 'alpha'] = dD_dCD * dCD_dalpha
J['drag', 'v'] = c_D * S * rho * v
J['drag', 'rho'] = .5 * c_D * S * v ** 2
J['lift', 'alpha'] = dL_dCL * dCL_dalpha
J['lift', 'v'] = c_L * S * rho * v
J['lift', 'rho'] = .5 * c_L * S * v ** 2


Below is the code for the heating component:

import numpy as np
import openmdao.api as om

class AerodynamicHeating(om.ExplicitComponent):
"""
Defines the Aerodynamic heating equations for the shuttle reentry problem.

References
----------
.. [1] Betts, John T., Practical Methods for Optimal Control and Estimation Using Nonlinear
Programming, p. 248, 2010.
"""

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

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

self.add_input('v', val=np.ones(nn), desc='velocity of shuttle', units='ft/s')
self.add_input('alpha', val=np.ones(nn), desc='angle of attack of shuttle',
units='deg')

desc='aerodynamic heating on leading edge of shuttle',
units='Btu/ft**2/s')

partial_range = np.arange(nn)

self.declare_partials('q', 'rho', rows=partial_range, cols=partial_range)
self.declare_partials('q', 'v', rows=partial_range, cols=partial_range)
self.declare_partials('q', 'alpha', rows=partial_range, cols=partial_range)

def compute(self, inputs, outputs):
rho = inputs['rho']
v = inputs['v']
alpha = inputs['alpha']
c_0 = 1.0672181
c_1 = -0.19213774e-1
c_2 = 0.21286289e-3
c_3 = -0.10117249e-5

q_r = 17700.0 * np.sqrt(rho) * (0.0001 * v) ** 3.07
q_a = c_0 + c_1 * alpha + c_2 * alpha ** 2 + c_3 * alpha ** 3

outputs['q'] = q_r * q_a

def compute_partials(self, inputs, partials):
rho = inputs['rho']
v = inputs['v']
alpha = inputs['alpha']
c_0 = 1.0672181
c_1 = -.19213774e-1
c_2 = .21286289e-3
c_3 = -.10117249e-5

sqrt_rho = np.sqrt(rho)

q_r = 17700 * sqrt_rho * (.0001 * v) ** 3.07
q_a = c_0 + c_1 * alpha + c_2 * alpha ** 2 + c_3 * alpha ** 3

dqr_drho = 0.5 * q_r / rho
dqr_dv = 17700 * sqrt_rho * 0.0001 * 3.07 * (0.0001 * v) ** 2.07

dqa_dalpha = c_1 + 2 * c_2 * alpha + 3 * c_3 * alpha ** 2

partials['q', 'rho'] = dqr_drho * q_a
partials['q', 'v'] = dqr_dv * q_a
partials['q', 'alpha'] = dqa_dalpha * q_r


Below is the code for the component containing the equations of motion:

import numpy as np
from openmdao.api import ExplicitComponent, Problem

class FlightDynamics(ExplicitComponent):
"""
Defines the flight dynamics for the shuttle reentry problem.

References
----------
.. [1] Betts, John T., Practical Methods for Optimal Control and Estimation Using Nonlinear
Programming, p. 247, 2010.
"""

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

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

self.add_input('h', val=np.ones(nn), desc='altitude of shuttle', units='ft')
self.add_input('v', val=np.ones(nn), desc='velocity of shuttle', units='ft/s')
self.add_input('lift', val=np.ones(nn), desc='lift on shuttle', units='lb')
self.add_input('drag', val=np.ones(nn), desc='drag on shuttle', units='lb')

self.add_output('hdot', val=np.ones(nn), desc='rate of change of altitude',
units='ft/s')
desc='rate of change of flight path angle', units='rad/s')
self.add_output('phidot', val=np.ones(nn), desc='rate of change of longitude',
self.add_output('psidot', val=np.ones(nn), desc='rate of change of azimuthal angle',
self.add_output('vdot', val=np.ones(nn), desc='rate of change of velocity',
units='ft/s**2')

partial_range = np.arange(nn, dtype=int)

self.declare_partials('hdot', 'v', rows=partial_range, cols=partial_range)
self.declare_partials('hdot', 'gamma', rows=partial_range, cols=partial_range)

self.declare_partials('phidot', 'v', rows=partial_range, cols=partial_range)
self.declare_partials('phidot', 'h', rows=partial_range, cols=partial_range)
self.declare_partials('phidot', 'gamma', rows=partial_range, cols=partial_range)
self.declare_partials('phidot', 'psi', rows=partial_range, cols=partial_range)
self.declare_partials('phidot', 'theta', rows=partial_range, cols=partial_range)

self.declare_partials('psidot', 'v', rows=partial_range, cols=partial_range)
self.declare_partials('psidot', 'gamma', rows=partial_range, cols=partial_range)
self.declare_partials('psidot', 'h', rows=partial_range, cols=partial_range)
self.declare_partials('psidot', 'beta', rows=partial_range, cols=partial_range)
self.declare_partials('psidot', 'theta', rows=partial_range, cols=partial_range)
self.declare_partials('psidot', 'psi', rows=partial_range, cols=partial_range)
self.declare_partials('psidot', 'lift', rows=partial_range, cols=partial_range)

self.declare_partials('vdot', 'drag', rows=partial_range, cols=partial_range)
self.declare_partials('vdot', 'gamma', rows=partial_range, cols=partial_range)
self.declare_partials('vdot', 'h', rows=partial_range, cols=partial_range)

def compute(self, inputs, outputs):
v = inputs['v']
gamma = inputs['gamma']
theta = inputs['theta']
lift = inputs['lift']
drag = inputs['drag']
h = inputs['h']
beta = inputs['beta']
psi = inputs['psi']
g_0 = 32.174
w = 203000
R_e = 20902900
mu = .14076539e17
s_beta = np.sin(beta)
c_beta = np.cos(beta)
s_gamma = np.sin(gamma)
c_gamma = np.cos(gamma)
s_psi = np.sin(psi)
c_psi = np.cos(psi)
c_theta = np.cos(theta)
s_theta = np.sin(theta)
r = R_e + h
m = w / g_0
g = mu / r ** 2

outputs['hdot'] = v * s_gamma
outputs['gammadot'] = lift / (m * v) * c_beta + c_gamma * (v / r - g / v)
outputs['phidot'] = v / r * c_gamma * s_psi / c_theta
outputs['psidot'] = lift * s_beta / (m * v * c_gamma) + \
v * c_gamma * s_psi * s_theta / (r * c_theta)
outputs['thetadot'] = c_gamma * c_psi * v / r
outputs['vdot'] = -drag / m - g * s_gamma

def compute_partials(self, inputs, J):
v = inputs['v']
gamma = inputs['gamma']
theta = inputs['theta']
lift = inputs['lift']
h = inputs['h']
beta = inputs['beta']
psi = inputs['psi']
g_0 = 32.174
w = 203000
R_e = 20902900
mu = .14076539e17
s_beta = np.sin(beta)
c_beta = np.cos(beta)
s_gamma = np.sin(gamma)
c_gamma = np.cos(gamma)
s_psi = np.sin(psi)
c_psi = np.cos(psi)
c_theta = np.cos(theta)
s_theta = np.sin(theta)
r = R_e + h
m = w / g_0
g = mu / r ** 2

J['hdot', 'v'] = s_gamma
J['hdot', 'gamma'] = v * c_gamma

J['gammadot', 'lift'] = c_beta / (m * v)
J['gammadot', 'h'] = c_gamma * (-v / r ** 2 + 2 * mu / (r ** 3 * v))
J['gammadot', 'beta'] = -lift / (m * v) * s_beta
J['gammadot', 'gamma'] = -s_gamma * (v / r - g / v)
J['gammadot', 'v'] = -lift / (m * v ** 2) * c_beta + c_gamma * (1 / r + g / v ** 2)

J['phidot', 'v'] = c_gamma * s_psi / (c_theta * r)
J['phidot', 'h'] = -v / r ** 2 * c_gamma * s_psi / c_theta
J['phidot', 'gamma'] = -v / r * s_gamma * s_psi / c_theta
J['phidot', 'psi'] = v / r * c_gamma * c_psi / c_theta
J['phidot', 'theta'] = v / r * c_gamma * s_psi / (c_theta ** 2) * s_theta

J['psidot', 'v'] = -lift * s_beta / (m * c_gamma * v ** 2) + \
c_gamma * s_psi * s_theta / (r * c_theta)
J['psidot', 'gamma'] = lift * s_beta / (m * v * c_gamma ** 2) * s_gamma - \
v * s_gamma * s_psi * s_theta / (r * c_theta)
J['psidot', 'h'] = -v * c_gamma * s_psi * s_theta / (c_theta * r ** 2)
J['psidot', 'beta'] = lift * c_beta / (m * v * c_gamma)
J['psidot', 'theta'] = v * c_gamma * s_psi / (r * c_theta ** 2)
J['psidot', 'psi'] = v * c_gamma * c_psi * s_theta / (r * c_theta)
J['psidot', 'lift'] = s_beta / (m * v * c_gamma)

J['thetadot', 'v'] = c_gamma * c_psi / r
J['thetadot', 'h'] = -v / r ** 2 * c_gamma * c_psi
J['thetadot', 'gamma'] = -v / r * s_gamma * c_psi
J['thetadot', 'psi'] = -v / r * c_gamma * s_psi

J['vdot', 'h'] = 2 * s_gamma * mu / r ** 3
J['vdot', 'drag'] = -1 / m
J['vdot', 'gamma'] = -g * c_gamma


## Defining the ODE#

Below is the code for the top level ode group that will be fed to dymos:

from openmdao.api import Group

class ShuttleODE(Group):
"""
The ODE for the Shuttle reentry problem.

References
----------
.. [1] Betts, John T., Practical Methods for Optimal Control and Estimation Using Nonlinear
Programming, p. 248, 2010.
"""

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

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

promotes_inputs=['h'], promotes_outputs=['rho'])
promotes_inputs=['alpha', 'v', 'rho'],
promotes_outputs=['lift', 'drag'])
promotes_inputs=['rho', 'v', 'alpha'], promotes_outputs=['q'])
promotes_inputs=['beta', 'gamma', 'h', 'psi', 'theta', 'v', 'lift',
'drag'],
'vdot'])


## Building and running the problem#

The following code is the dymos implementation of the model. As the code shows, there are six states, two controls, and one constraint in the model. The states are $$h, v, \phi, \gamma, \theta,$$ and $$\psi$$. The two controls are $$\alpha$$ and $$\beta$$, and the constraint is $$q$$.

import openmdao.api as om
import dymos as dm

from dymos.examples.shuttle_reentry.shuttle_ode import ShuttleODE
from dymos.examples.plotting import plot_results
import matplotlib.pyplot as plt

# Instantiate the problem, add the driver, and allow it to use coloring
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.declare_coloring()
p.driver.options['optimizer'] = 'SLSQP'

# Instantiate the trajectory and add a phase to it
dm.Phase(ode_class=ShuttleODE,

phase0.set_time_options(fix_initial=True, units='s', duration_ref=200)
lower=0, ref0=75000, ref=300000, defect_ref=1000)
lower=-89. * np.pi / 180, upper=89. * np.pi / 180)
rate_source='phidot', lower=0, upper=89. * np.pi / 180)
rate_source='psidot', lower=0, upper=90. * np.pi / 180)
lower=-89. * np.pi / 180, upper=89. * np.pi / 180)
rate_source='vdot', lower=0, ref0=2500, ref=25000)
phase0.add_control('beta', units='rad', opt=True, lower=-89 * np.pi / 180, upper=1 * np.pi / 180, )

# The original implementation by Betts includes a heating rate path constraint.
# This will work with the SNOPT optimizer but SLSQP has difficulty converging the solution.

p.setup(check=True)

p.set_val('traj.phase0.t_initial', 0, units='s')
p.set_val('traj.phase0.t_duration', 2000, units='s')

p.set_val('traj.phase0.states:h',
phase0.interp('h', [260000, 80000]), units='ft')
p.set_val('traj.phase0.states:gamma',
phase0.interp('gamma', [-1, -5]), units='deg')
p.set_val('traj.phase0.states:phi',
phase0.interp('phi', [0, 75]), units='deg')
p.set_val('traj.phase0.states:psi',
phase0.interp('psi', [90, 10]), units='deg')
p.set_val('traj.phase0.states:theta',
phase0.interp('theta', [0, 25]), units='deg')
p.set_val('traj.phase0.states:v',
phase0.interp('v', [25600, 2500]), units='ft/s')

p.set_val('traj.phase0.controls:alpha',
phase0.interp('alpha', ys=[17.4, 17.4]), units='deg')
p.set_val('traj.phase0.controls:beta',
phase0.interp('beta', ys=[-75, 0]), units='deg')

# Run the driver
dm.run_problem(p, simulate=True)

--- Constraint Report [traj] ---
--- phase0 ---
None

INFO: checking out_of_order

INFO:check_config:checking out_of_order

INFO: checking system

INFO:check_config:checking system

INFO: checking solvers

INFO:check_config:checking solvers

INFO: checking dup_inputs

INFO:check_config:checking dup_inputs

INFO: checking missing_recorders

INFO:check_config:checking missing_recorders

WARNING: The Problem has no recorder of any kind attached

WARNING:check_config:The Problem has no recorder of any kind attached

INFO: checking unserializable_options

INFO:check_config:checking unserializable_options

INFO: checking comp_has_no_outputs

INFO:check_config:checking comp_has_no_outputs

INFO: checking auto_ivc_warnings

INFO:check_config:checking auto_ivc_warnings

Model viewer data has already been recorded for Driver.
INFO: checking out_of_order

INFO:check_config:checking out_of_order

INFO: checking system

INFO:check_config:checking system

INFO: checking solvers

INFO:check_config:checking solvers

INFO: checking dup_inputs

INFO:check_config:checking dup_inputs

INFO: checking missing_recorders

INFO:check_config:checking missing_recorders

WARNING: The Problem has no recorder of any kind attached

WARNING:check_config:The Problem has no recorder of any kind attached

INFO: checking unserializable_options

INFO:check_config:checking unserializable_options

INFO: checking comp_has_no_outputs

INFO:check_config:checking comp_has_no_outputs

INFO: checking auto_ivc_warnings

INFO:check_config:checking auto_ivc_warnings

Model viewer data has already been recorded for Driver.
INFO: checking out_of_order

INFO:check_config:checking out_of_order

INFO: checking system

INFO:check_config:checking system

INFO: checking solvers

INFO:check_config:checking solvers

INFO: checking dup_inputs

INFO:check_config:checking dup_inputs

INFO: checking missing_recorders

INFO:check_config:checking missing_recorders

WARNING: The Problem has no recorder of any kind attached

WARNING:check_config:The Problem has no recorder of any kind attached

INFO: checking unserializable_options

INFO:check_config:checking unserializable_options

INFO: checking comp_has_no_outputs

INFO:check_config:checking comp_has_no_outputs

INFO: checking auto_ivc_warnings

INFO:check_config:checking auto_ivc_warnings

Full total jacobian was computed 3 times, taking 1.129180 seconds.
Total jacobian shape: (327, 358)

Jacobian shape: (327, 358)  ( 2.30% nonzero)
FWD solves: 20   REV solves: 0
Total colors vs. total size: 20 vs 358  (94.4% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 1.129180 sec.
Time to compute coloring: 0.385019 sec.
Memory to compute coloring: 0.375000 MB.

/usr/share/miniconda/envs/test/lib/python3.10/site-packages/dymos/examples/shuttle_reentry/heating_comp.py:45: RuntimeWarning: invalid value encountered in power
q_r = 17700.0 * np.sqrt(rho) * (0.0001 * v) ** 3.07

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

Solution:
--------------------------------------------------------------------------------
Total Time:                   30.6832
User Objective Time :       0.5297
User Sensitivity Time :     4.0763
Interface Time :            1.2109
Opt Solver Time:           24.8662
Calls to Objective Function :     274
Calls to Sens Function :          141

Objectives
Index  Name                                                    Value
0  traj.phases.phase0.indep_states.states:theta    -5.957515E+01

Variables (c - continuous, i - integer, d - discrete)
Index  Name                                                                Type      Lower Bound            Value      Upper Bound     Status
0  traj.phase0.t_duration_0                                               c    -5.000000E+18     1.004142E+01     5.000000E+18
1  traj.phases.phase0.indep_states.states:h_0                             c    -3.333333E-01     7.284159E-01     4.444444E+15
2  traj.phases.phase0.indep_states.states:h_1                             c    -3.333333E-01     6.156161E-01     4.444444E+15
3  traj.phases.phase0.indep_states.states:h_2                             c    -3.333333E-01     5.881392E-01     4.444444E+15
4  traj.phases.phase0.indep_states.states:h_3                             c    -3.333333E-01     5.549055E-01     4.444444E+15
5  traj.phases.phase0.indep_states.states:h_4                             c    -3.333333E-01     5.678795E-01     4.444444E+15
6  traj.phases.phase0.indep_states.states:h_5                             c    -3.333333E-01     5.831409E-01     4.444444E+15
7  traj.phases.phase0.indep_states.states:h_6                             c    -3.333333E-01     6.121451E-01     4.444444E+15
8  traj.phases.phase0.indep_states.states:h_7                             c    -3.333333E-01     6.265189E-01     4.444444E+15
9  traj.phases.phase0.indep_states.states:h_8                             c    -3.333333E-01     6.206406E-01     4.444444E+15
10  traj.phases.phase0.indep_states.states:h_9                             c    -3.333333E-01     5.951359E-01     4.444444E+15
11  traj.phases.phase0.indep_states.states:h_10                            c    -3.333333E-01     5.502189E-01     4.444444E+15
12  traj.phases.phase0.indep_states.states:h_11                            c    -3.333333E-01     5.392159E-01     4.444444E+15
13  traj.phases.phase0.indep_states.states:h_12                            c    -3.333333E-01     5.283045E-01     4.444444E+15
14  traj.phases.phase0.indep_states.states:h_13                            c    -3.333333E-01     5.314225E-01     4.444444E+15
15  traj.phases.phase0.indep_states.states:h_14                            c    -3.333333E-01     5.333901E-01     4.444444E+15
16  traj.phases.phase0.indep_states.states:h_15                            c    -3.333333E-01     5.294809E-01     4.444444E+15
17  traj.phases.phase0.indep_states.states:h_16                            c    -3.333333E-01     5.100674E-01     4.444444E+15
18  traj.phases.phase0.indep_states.states:h_17                            c    -3.333333E-01     5.014967E-01     4.444444E+15
19  traj.phases.phase0.indep_states.states:h_18                            c    -3.333333E-01     4.869279E-01     4.444444E+15
20  traj.phases.phase0.indep_states.states:h_19                            c    -3.333333E-01     4.779607E-01     4.444444E+15
21  traj.phases.phase0.indep_states.states:h_20                            c    -3.333333E-01     4.777471E-01     4.444444E+15
22  traj.phases.phase0.indep_states.states:h_21                            c    -3.333333E-01     4.727101E-01     4.444444E+15
23  traj.phases.phase0.indep_states.states:h_22                            c    -3.333333E-01     4.551821E-01     4.444444E+15
24  traj.phases.phase0.indep_states.states:h_23                            c    -3.333333E-01     4.469347E-01     4.444444E+15
25  traj.phases.phase0.indep_states.states:h_24                            c    -3.333333E-01     4.317130E-01     4.444444E+15
26  traj.phases.phase0.indep_states.states:h_25                            c    -3.333333E-01     4.192045E-01     4.444444E+15
27  traj.phases.phase0.indep_states.states:h_26                            c    -3.333333E-01     4.173268E-01     4.444444E+15
28  traj.phases.phase0.indep_states.states:h_27                            c    -3.333333E-01     4.089570E-01     4.444444E+15
29  traj.phases.phase0.indep_states.states:h_28                            c    -3.333333E-01     3.894636E-01     4.444444E+15
30  traj.phases.phase0.indep_states.states:h_29                            c    -3.333333E-01     3.816042E-01     4.444444E+15
31  traj.phases.phase0.indep_states.states:h_30                            c    -3.333333E-01     3.661114E-01     4.444444E+15
32  traj.phases.phase0.indep_states.states:h_31                            c    -3.333333E-01     3.470618E-01     4.444444E+15
33  traj.phases.phase0.indep_states.states:h_32                            c    -3.333333E-01     3.409513E-01     4.444444E+15
34  traj.phases.phase0.indep_states.states:h_33                            c    -3.333333E-01     3.245332E-01     4.444444E+15
35  traj.phases.phase0.indep_states.states:h_34                            c    -3.333333E-01     2.998636E-01     4.444444E+15
36  traj.phases.phase0.indep_states.states:h_35                            c    -3.333333E-01     2.920833E-01     4.444444E+15
37  traj.phases.phase0.indep_states.states:h_36                            c    -3.333333E-01     2.728221E-01     4.444444E+15
38  traj.phases.phase0.indep_states.states:h_37                            c    -3.333333E-01     2.423549E-01     4.444444E+15
39  traj.phases.phase0.indep_states.states:h_38                            c    -3.333333E-01     2.319041E-01     4.444444E+15
40  traj.phases.phase0.indep_states.states:h_39                            c    -3.333333E-01     2.075987E-01     4.444444E+15
41  traj.phases.phase0.indep_states.states:h_40                            c    -3.333333E-01     1.651010E-01     4.444444E+15
42  traj.phases.phase0.indep_states.states:h_41                            c    -3.333333E-01     1.477369E-01     4.444444E+15
43  traj.phases.phase0.indep_states.states:h_42                            c    -3.333333E-01     1.041282E-01     4.444444E+15
44  traj.phases.phase0.indep_states.states:h_43                            c    -3.333333E-01     4.169697E-02     4.444444E+15
45  traj.phases.phase0.indep_states.states:gamma_0                         c    -1.553343E+00    -1.691899E-02     1.553343E+00
46  traj.phases.phase0.indep_states.states:gamma_1                         c    -1.553343E+00    -1.282756E-02     1.553343E+00
47  traj.phases.phase0.indep_states.states:gamma_2                         c    -1.553343E+00    -1.023681E-02     1.553343E+00
48  traj.phases.phase0.indep_states.states:gamma_3                         c    -1.553343E+00    -2.575163E-03     1.553343E+00
49  traj.phases.phase0.indep_states.states:gamma_4                         c    -1.553343E+00     5.849400E-03     1.553343E+00
50  traj.phases.phase0.indep_states.states:gamma_5                         c    -1.553343E+00     6.424899E-03     1.553343E+00
51  traj.phases.phase0.indep_states.states:gamma_6                         c    -1.553343E+00     4.800267E-03     1.553343E+00
52  traj.phases.phase0.indep_states.states:gamma_7                         c    -1.553343E+00    -1.346038E-03     1.553343E+00
53  traj.phases.phase0.indep_states.states:gamma_8                         c    -1.553343E+00    -3.415126E-03     1.553343E+00
54  traj.phases.phase0.indep_states.states:gamma_9                         c    -1.553343E+00    -6.633955E-03     1.553343E+00
55  traj.phases.phase0.indep_states.states:gamma_10                        c    -1.553343E+00    -6.054919E-03     1.553343E+00
56  traj.phases.phase0.indep_states.states:gamma_11                        c    -1.553343E+00    -4.311191E-03     1.553343E+00
57  traj.phases.phase0.indep_states.states:gamma_12                        c    -1.553343E+00    -7.188229E-04     1.553343E+00
58  traj.phases.phase0.indep_states.states:gamma_13                        c    -1.553343E+00     1.108953E-03     1.553343E+00
59  traj.phases.phase0.indep_states.states:gamma_14                        c    -1.553343E+00     3.170369E-04     1.553343E+00
60  traj.phases.phase0.indep_states.states:gamma_15                        c    -1.553343E+00    -2.055009E-03     1.553343E+00
61  traj.phases.phase0.indep_states.states:gamma_16                        c    -1.553343E+00    -4.490201E-03     1.553343E+00
62  traj.phases.phase0.indep_states.states:gamma_17                        c    -1.553343E+00    -4.415397E-03     1.553343E+00
63  traj.phases.phase0.indep_states.states:gamma_18                        c    -1.553343E+00    -2.808303E-03     1.553343E+00
64  traj.phases.phase0.indep_states.states:gamma_19                        c    -1.553343E+00    -5.047880E-04     1.553343E+00
65  traj.phases.phase0.indep_states.states:gamma_20                        c    -1.553343E+00    -5.261232E-04     1.553343E+00
66  traj.phases.phase0.indep_states.states:gamma_21                        c    -1.553343E+00    -2.253831E-03     1.553343E+00
67  traj.phases.phase0.indep_states.states:gamma_22                        c    -1.553343E+00    -5.020436E-03     1.553343E+00
68  traj.phases.phase0.indep_states.states:gamma_23                        c    -1.553343E+00    -5.225160E-03     1.553343E+00
69  traj.phases.phase0.indep_states.states:gamma_24                        c    -1.553343E+00    -3.871730E-03     1.553343E+00
70  traj.phases.phase0.indep_states.states:gamma_25                        c    -1.553343E+00    -1.772826E-03     1.553343E+00
71  traj.phases.phase0.indep_states.states:gamma_26                        c    -1.553343E+00    -1.892008E-03     1.553343E+00
72  traj.phases.phase0.indep_states.states:gamma_27                        c    -1.553343E+00    -3.795759E-03     1.553343E+00
73  traj.phases.phase0.indep_states.states:gamma_28                        c    -1.553343E+00    -6.370021E-03     1.553343E+00
74  traj.phases.phase0.indep_states.states:gamma_29                        c    -1.553343E+00    -6.429732E-03     1.553343E+00
75  traj.phases.phase0.indep_states.states:gamma_30                        c    -1.553343E+00    -5.801696E-03     1.553343E+00
76  traj.phases.phase0.indep_states.states:gamma_31                        c    -1.553343E+00    -6.055770E-03     1.553343E+00
77  traj.phases.phase0.indep_states.states:gamma_32                        c    -1.553343E+00    -6.903779E-03     1.553343E+00
78  traj.phases.phase0.indep_states.states:gamma_33                        c    -1.553343E+00    -8.421686E-03     1.553343E+00
79  traj.phases.phase0.indep_states.states:gamma_34                        c    -1.553343E+00    -9.713284E-03     1.553343E+00
80  traj.phases.phase0.indep_states.states:gamma_35                        c    -1.553343E+00    -1.006022E-02     1.553343E+00
81  traj.phases.phase0.indep_states.states:gamma_36                        c    -1.553343E+00    -1.259546E-02     1.553343E+00
82  traj.phases.phase0.indep_states.states:gamma_37                        c    -1.553343E+00    -1.659486E-02     1.553343E+00
83  traj.phases.phase0.indep_states.states:gamma_38                        c    -1.553343E+00    -1.736904E-02     1.553343E+00
84  traj.phases.phase0.indep_states.states:gamma_39                        c    -1.553343E+00    -2.171651E-02     1.553343E+00
85  traj.phases.phase0.indep_states.states:gamma_40                        c    -1.553343E+00    -3.753268E-02     1.553343E+00
86  traj.phases.phase0.indep_states.states:gamma_41                        c    -1.553343E+00    -4.535755E-02     1.553343E+00
87  traj.phases.phase0.indep_states.states:gamma_42                        c    -1.553343E+00    -5.729613E-02     1.553343E+00
88  traj.phases.phase0.indep_states.states:gamma_43                        c    -1.553343E+00    -7.666873E-02     1.553343E+00
89  traj.phases.phase0.indep_states.states:phi_0                           c     0.000000E+00     5.749288E-02     1.553343E+00
90  traj.phases.phase0.indep_states.states:phi_1                           c     0.000000E+00     1.364708E-01     1.553343E+00
91  traj.phases.phase0.indep_states.states:phi_2                           c     0.000000E+00     1.612834E-01     1.553343E+00
92  traj.phases.phase0.indep_states.states:phi_3                           c     0.000000E+00     2.173349E-01     1.553343E+00
93  traj.phases.phase0.indep_states.states:phi_4                           c     0.000000E+00     2.926232E-01     1.553343E+00
94  traj.phases.phase0.indep_states.states:phi_5                           c     0.000000E+00     3.158916E-01     1.553343E+00
95  traj.phases.phase0.indep_states.states:phi_6                           c     0.000000E+00     3.685435E-01     1.553343E+00
96  traj.phases.phase0.indep_states.states:phi_7                           c     0.000000E+00     4.398906E-01     1.553343E+00
97  traj.phases.phase0.indep_states.states:phi_8                           c     0.000000E+00     4.622262E-01     1.553343E+00
98  traj.phases.phase0.indep_states.states:phi_9                           c     0.000000E+00     5.128565E-01     1.553343E+00
99  traj.phases.phase0.indep_states.states:phi_10                          c     0.000000E+00     5.812393E-01     1.553343E+00
100  traj.phases.phase0.indep_states.states:phi_11                          c     0.000000E+00     6.024325E-01     1.553343E+00
101  traj.phases.phase0.indep_states.states:phi_12                          c     0.000000E+00     6.498909E-01     1.553343E+00
102  traj.phases.phase0.indep_states.states:phi_13                          c     0.000000E+00     7.129270E-01     1.553343E+00
103  traj.phases.phase0.indep_states.states:phi_14                          c     0.000000E+00     7.322843E-01     1.553343E+00
104  traj.phases.phase0.indep_states.states:phi_15                          c     0.000000E+00     7.756898E-01     1.553343E+00
105  traj.phases.phase0.indep_states.states:phi_16                          c     0.000000E+00     8.333483E-01     1.553343E+00
106  traj.phases.phase0.indep_states.states:phi_17                          c     0.000000E+00     8.510380E-01     1.553343E+00
107  traj.phases.phase0.indep_states.states:phi_18                          c     0.000000E+00     8.903591E-01     1.553343E+00
108  traj.phases.phase0.indep_states.states:phi_19                          c     0.000000E+00     9.418062E-01     1.553343E+00
109  traj.phases.phase0.indep_states.states:phi_20                          c     0.000000E+00     9.573849E-01     1.553343E+00
110  traj.phases.phase0.indep_states.states:phi_21                          c     0.000000E+00     9.918853E-01     1.553343E+00
111  traj.phases.phase0.indep_states.states:phi_22                          c     0.000000E+00     1.036771E+00     1.553343E+00
112  traj.phases.phase0.indep_states.states:phi_23                          c     0.000000E+00     1.050316E+00     1.553343E+00
113  traj.phases.phase0.indep_states.states:phi_24                          c     0.000000E+00     1.080000E+00     1.553343E+00
114  traj.phases.phase0.indep_states.states:phi_25                          c     0.000000E+00     1.117849E+00     1.553343E+00
115  traj.phases.phase0.indep_states.states:phi_26                          c     0.000000E+00     1.129060E+00     1.553343E+00
116  traj.phases.phase0.indep_states.states:phi_27                          c     0.000000E+00     1.153438E+00     1.553343E+00
117  traj.phases.phase0.indep_states.states:phi_28                          c     0.000000E+00     1.184106E+00     1.553343E+00
118  traj.phases.phase0.indep_states.states:phi_29                          c     0.000000E+00     1.193097E+00     1.553343E+00
119  traj.phases.phase0.indep_states.states:phi_30                          c     0.000000E+00     1.212321E+00     1.553343E+00
120  traj.phases.phase0.indep_states.states:phi_31                          c     0.000000E+00     1.235760E+00     1.553343E+00
121  traj.phases.phase0.indep_states.states:phi_32                          c     0.000000E+00     1.242439E+00     1.553343E+00
122  traj.phases.phase0.indep_states.states:phi_33                          c     0.000000E+00     1.256447E+00     1.553343E+00
123  traj.phases.phase0.indep_states.states:phi_34                          c     0.000000E+00     1.272889E+00     1.553343E+00
124  traj.phases.phase0.indep_states.states:phi_35                          c     0.000000E+00     1.277414E+00     1.553343E+00
125  traj.phases.phase0.indep_states.states:phi_36                          c     0.000000E+00     1.286608E+00     1.553343E+00
126  traj.phases.phase0.indep_states.states:phi_37                          c     0.000000E+00     1.296777E+00     1.553343E+00
127  traj.phases.phase0.indep_states.states:phi_38                          c     0.000000E+00     1.299423E+00     1.553343E+00
128  traj.phases.phase0.indep_states.states:phi_39                          c     0.000000E+00     1.304525E+00     1.553343E+00
129  traj.phases.phase0.indep_states.states:phi_40                          c     0.000000E+00     1.309634E+00     1.553343E+00
130  traj.phases.phase0.indep_states.states:phi_41                          c     0.000000E+00     1.310848E+00     1.553343E+00
131  traj.phases.phase0.indep_states.states:phi_42                          c     0.000000E+00     1.313014E+00     1.553343E+00
132  traj.phases.phase0.indep_states.states:phi_43                          c     0.000000E+00     1.314909E+00     1.553343E+00
133  traj.phases.phase0.indep_states.states:phi_44                          c     0.000000E+00     1.315328E+00     1.553343E+00
134  traj.phases.phase0.indep_states.states:psi_0                           c     0.000000E+00     1.565674E+00     1.570796E+00
135  traj.phases.phase0.indep_states.states:psi_1                           c     0.000000E+00     1.545940E+00     1.570796E+00
136  traj.phases.phase0.indep_states.states:psi_2                           c     0.000000E+00     1.534776E+00     1.570796E+00
137  traj.phases.phase0.indep_states.states:psi_3                           c     0.000000E+00     1.500315E+00     1.570796E+00
138  traj.phases.phase0.indep_states.states:psi_4                           c     0.000000E+00     1.449365E+00     1.570796E+00
139  traj.phases.phase0.indep_states.states:psi_5                           c     0.000000E+00     1.436820E+00     1.570796E+00
140  traj.phases.phase0.indep_states.states:psi_6                           c     0.000000E+00     1.414016E+00     1.570796E+00
141  traj.phases.phase0.indep_states.states:psi_7                           c     0.000000E+00     1.390786E+00     1.570796E+00
142  traj.phases.phase0.indep_states.states:psi_8                           c     0.000000E+00     1.383873E+00     1.570796E+00
143  traj.phases.phase0.indep_states.states:psi_9                           c     0.000000E+00     1.365824E+00     1.570796E+00
144  traj.phases.phase0.indep_states.states:psi_10                          c     0.000000E+00     1.331841E+00     1.570796E+00
145  traj.phases.phase0.indep_states.states:psi_11                          c     0.000000E+00     1.317938E+00     1.570796E+00
146  traj.phases.phase0.indep_states.states:psi_12                          c     0.000000E+00     1.284235E+00     1.570796E+00
147  traj.phases.phase0.indep_states.states:psi_13                          c     0.000000E+00     1.238927E+00     1.570796E+00
148  traj.phases.phase0.indep_states.states:psi_14                          c     0.000000E+00     1.226295E+00     1.570796E+00
149  traj.phases.phase0.indep_states.states:psi_15                          c     0.000000E+00     1.198170E+00     1.570796E+00
150  traj.phases.phase0.indep_states.states:psi_16                          c     0.000000E+00     1.157989E+00     1.570796E+00
151  traj.phases.phase0.indep_states.states:psi_17                          c     0.000000E+00     1.143957E+00     1.570796E+00
152  traj.phases.phase0.indep_states.states:psi_18                          c     0.000000E+00     1.109316E+00     1.570796E+00
153  traj.phases.phase0.indep_states.states:psi_19                          c     0.000000E+00     1.059696E+00     1.570796E+00
154  traj.phases.phase0.indep_states.states:psi_20                          c     0.000000E+00     1.044516E+00     1.570796E+00
155  traj.phases.phase0.indep_states.states:psi_21                          c     0.000000E+00     1.011084E+00     1.570796E+00
156  traj.phases.phase0.indep_states.states:psi_22                          c     0.000000E+00     9.643017E-01     1.570796E+00
157  traj.phases.phase0.indep_states.states:psi_23                          c     0.000000E+00     9.484961E-01     1.570796E+00
158  traj.phases.phase0.indep_states.states:psi_24                          c     0.000000E+00     9.097985E-01     1.570796E+00
159  traj.phases.phase0.indep_states.states:psi_25                          c     0.000000E+00     8.544317E-01     1.570796E+00
160  traj.phases.phase0.indep_states.states:psi_26                          c     0.000000E+00     8.372756E-01     1.570796E+00
161  traj.phases.phase0.indep_states.states:psi_27                          c     0.000000E+00     7.990071E-01     1.570796E+00
162  traj.phases.phase0.indep_states.states:psi_28                          c     0.000000E+00     7.453695E-01     1.570796E+00
163  traj.phases.phase0.indep_states.states:psi_29                          c     0.000000E+00     7.275174E-01     1.570796E+00
164  traj.phases.phase0.indep_states.states:psi_30                          c     0.000000E+00     6.850174E-01     1.570796E+00
165  traj.phases.phase0.indep_states.states:psi_31                          c     0.000000E+00     6.246545E-01     1.570796E+00
166  traj.phases.phase0.indep_states.states:psi_32                          c     0.000000E+00     6.055319E-01     1.570796E+00
167  traj.phases.phase0.indep_states.states:psi_33                          c     0.000000E+00     5.612272E-01     1.570796E+00
168  traj.phases.phase0.indep_states.states:psi_34                          c     0.000000E+00     4.989078E-01     1.570796E+00
169  traj.phases.phase0.indep_states.states:psi_35                          c     0.000000E+00     4.789250E-01     1.570796E+00
170  traj.phases.phase0.indep_states.states:psi_36                          c     0.000000E+00     4.332275E-01     1.570796E+00
171  traj.phases.phase0.indep_states.states:psi_37                          c     0.000000E+00     3.693714E-01     1.570796E+00
172  traj.phases.phase0.indep_states.states:psi_38                          c     0.000000E+00     3.488178E-01     1.570796E+00
173  traj.phases.phase0.indep_states.states:psi_39                          c     0.000000E+00     3.020497E-01     1.570796E+00
174  traj.phases.phase0.indep_states.states:psi_40                          c     0.000000E+00     2.396896E-01     1.570796E+00
175  traj.phases.phase0.indep_states.states:psi_41                          c     0.000000E+00     2.207489E-01     1.570796E+00
176  traj.phases.phase0.indep_states.states:psi_42                          c     0.000000E+00     1.786333E-01     1.570796E+00
177  traj.phases.phase0.indep_states.states:psi_43                          c     0.000000E+00     1.372729E-01     1.570796E+00
178  traj.phases.phase0.indep_states.states:psi_44                          c     0.000000E+00     1.318542E-01     1.570796E+00
179  traj.phases.phase0.indep_states.states:theta_0                         c    -1.553343E+00     1.108134E-04     1.553343E+00
180  traj.phases.phase0.indep_states.states:theta_1                         c    -1.553343E+00     1.195169E-03     1.553343E+00
181  traj.phases.phase0.indep_states.states:theta_2                         c    -1.553343E+00     1.925667E-03     1.553343E+00
182  traj.phases.phase0.indep_states.states:theta_3                         c    -1.553343E+00     4.901626E-03     1.553343E+00
183  traj.phases.phase0.indep_states.states:theta_4                         c    -1.553343E+00     1.211103E-02     1.553343E+00
184  traj.phases.phase0.indep_states.states:theta_5                         c    -1.553343E+00     1.515091E-02     1.553343E+00
185  traj.phases.phase0.indep_states.states:theta_6                         c    -1.553343E+00     2.287837E-02     1.553343E+00
186  traj.phases.phase0.indep_states.states:theta_7                         c    -1.553343E+00     3.506117E-02     1.553343E+00
187  traj.phases.phase0.indep_states.states:theta_8                         c    -1.553343E+00     3.918549E-02     1.553343E+00
188  traj.phases.phase0.indep_states.states:theta_9                         c    -1.553343E+00     4.920162E-02     1.553343E+00
189  traj.phases.phase0.indep_states.states:theta_10                        c    -1.553343E+00     6.453884E-02     1.553343E+00
190  traj.phases.phase0.indep_states.states:theta_11                        c    -1.553343E+00     6.983509E-02     1.553343E+00
191  traj.phases.phase0.indep_states.states:theta_12                        c    -1.553343E+00     8.291632E-02     1.553343E+00
192  traj.phases.phase0.indep_states.states:theta_13                        c    -1.553343E+00     1.029668E-01     1.553343E+00
193  traj.phases.phase0.indep_states.states:theta_14                        c    -1.553343E+00     1.097515E-01     1.553343E+00
194  traj.phases.phase0.indep_states.states:theta_15                        c    -1.553343E+00     1.259000E-01     1.553343E+00
195  traj.phases.phase0.indep_states.states:theta_16                        c    -1.553343E+00     1.495411E-01     1.553343E+00
196  traj.phases.phase0.indep_states.states:theta_17                        c    -1.553343E+00     1.573340E-01     1.553343E+00
197  traj.phases.phase0.indep_states.states:theta_18                        c    -1.553343E+00     1.757793E-01     1.553343E+00
198  traj.phases.phase0.indep_states.states:theta_19                        c    -1.553343E+00     2.024669E-01     1.553343E+00
199  traj.phases.phase0.indep_states.states:theta_20                        c    -1.553343E+00     2.111800E-01     1.553343E+00
200  traj.phases.phase0.indep_states.states:theta_21                        c    -1.553343E+00     2.314882E-01     1.553343E+00
201  traj.phases.phase0.indep_states.states:theta_22                        c    -1.553343E+00     2.601903E-01     1.553343E+00
202  traj.phases.phase0.indep_states.states:theta_23                        c    -1.553343E+00     2.694044E-01     1.553343E+00
203  traj.phases.phase0.indep_states.states:theta_24                        c    -1.553343E+00     2.907085E-01     1.553343E+00
204  traj.phases.phase0.indep_states.states:theta_25                        c    -1.553343E+00     3.203907E-01     1.553343E+00
205  traj.phases.phase0.indep_states.states:theta_26                        c    -1.553343E+00     3.298101E-01     1.553343E+00
206  traj.phases.phase0.indep_states.states:theta_27                        c    -1.553343E+00     3.513229E-01     1.553343E+00
207  traj.phases.phase0.indep_states.states:theta_28                        c    -1.553343E+00     3.807046E-01     1.553343E+00
208  traj.phases.phase0.indep_states.states:theta_29                        c    -1.553343E+00     3.898884E-01     1.553343E+00
209  traj.phases.phase0.indep_states.states:theta_30                        c    -1.553343E+00     4.106322E-01     1.553343E+00
210  traj.phases.phase0.indep_states.states:theta_31                        c    -1.553343E+00     4.384140E-01     1.553343E+00
211  traj.phases.phase0.indep_states.states:theta_32                        c    -1.553343E+00     4.469587E-01     1.553343E+00
212  traj.phases.phase0.indep_states.states:theta_33                        c    -1.553343E+00     4.659979E-01     1.553343E+00
213  traj.phases.phase0.indep_states.states:theta_34                        c    -1.553343E+00     4.908676E-01     1.553343E+00
214  traj.phases.phase0.indep_states.states:theta_35                        c    -1.553343E+00     4.983542E-01     1.553343E+00
215  traj.phases.phase0.indep_states.states:theta_36                        c    -1.553343E+00     5.147300E-01     1.553343E+00
216  traj.phases.phase0.indep_states.states:theta_37                        c    -1.553343E+00     5.354191E-01     1.553343E+00
217  traj.phases.phase0.indep_states.states:theta_38                        c    -1.553343E+00     5.414699E-01     1.553343E+00
218  traj.phases.phase0.indep_states.states:theta_39                        c    -1.553343E+00     5.543606E-01     1.553343E+00
219  traj.phases.phase0.indep_states.states:theta_40                        c    -1.553343E+00     5.698864E-01     1.553343E+00
220  traj.phases.phase0.indep_states.states:theta_41                        c    -1.553343E+00     5.742429E-01     1.553343E+00
221  traj.phases.phase0.indep_states.states:theta_42                        c    -1.553343E+00     5.832012E-01     1.553343E+00
222  traj.phases.phase0.indep_states.states:theta_43                        c    -1.553343E+00     5.931773E-01     1.553343E+00
223  traj.phases.phase0.indep_states.states:theta_44                        c    -1.553343E+00     5.957515E-01     1.553343E+00
224  traj.phases.phase0.indep_states.states:v_0                             c    -1.111111E-01     1.024611E+00     4.444444E+16
225  traj.phases.phase0.indep_states.states:v_1                             c    -1.111111E-01     1.013613E+00     4.444444E+16
226  traj.phases.phase0.indep_states.states:v_2                             c    -1.111111E-01     1.006946E+00     4.444444E+16
227  traj.phases.phase0.indep_states.states:v_3                             c    -1.111111E-01     9.859723E-01     4.444444E+16
228  traj.phases.phase0.indep_states.states:v_4                             c    -1.111111E-01     9.545183E-01     4.444444E+16
229  traj.phases.phase0.indep_states.states:v_5                             c    -1.111111E-01     9.466907E-01     4.444444E+16
230  traj.phases.phase0.indep_states.states:v_6                             c    -1.111111E-01     9.322266E-01     4.444444E+16
231  traj.phases.phase0.indep_states.states:v_7                             c    -1.111111E-01     9.170807E-01     4.444444E+16
232  traj.phases.phase0.indep_states.states:v_8                             c    -1.111111E-01     9.125230E-01     4.444444E+16
233  traj.phases.phase0.indep_states.states:v_9                             c    -1.111111E-01     9.005192E-01     4.444444E+16
234  traj.phases.phase0.indep_states.states:v_10                            c    -1.111111E-01     8.778468E-01     4.444444E+16
235  traj.phases.phase0.indep_states.states:v_11                            c    -1.111111E-01     8.685913E-01     4.444444E+16
236  traj.phases.phase0.indep_states.states:v_12                            c    -1.111111E-01     8.461902E-01     4.444444E+16
237  traj.phases.phase0.indep_states.states:v_13                            c    -1.111111E-01     8.155928E-01     4.444444E+16
238  traj.phases.phase0.indep_states.states:v_14                            c    -1.111111E-01     8.067919E-01     4.444444E+16
239  traj.phases.phase0.indep_states.states:v_15                            c    -1.111111E-01     7.868396E-01     4.444444E+16
240  traj.phases.phase0.indep_states.states:v_16                            c    -1.111111E-01     7.579292E-01     4.444444E+16
241  traj.phases.phase0.indep_states.states:v_17                            c    -1.111111E-01     7.478816E-01     4.444444E+16
242  traj.phases.phase0.indep_states.states:v_18                            c    -1.111111E-01     7.231767E-01     4.444444E+16
243  traj.phases.phase0.indep_states.states:v_19                            c    -1.111111E-01     6.874665E-01     4.444444E+16
244  traj.phases.phase0.indep_states.states:v_20                            c    -1.111111E-01     6.763243E-01     4.444444E+16
245  traj.phases.phase0.indep_states.states:v_21                            c    -1.111111E-01     6.513863E-01     4.444444E+16
246  traj.phases.phase0.indep_states.states:v_22                            c    -1.111111E-01     6.163239E-01     4.444444E+16
247  traj.phases.phase0.indep_states.states:v_23                            c    -1.111111E-01     6.046272E-01     4.444444E+16
248  traj.phases.phase0.indep_states.states:v_24                            c    -1.111111E-01     5.763639E-01     4.444444E+16
249  traj.phases.phase0.indep_states.states:v_25                            c    -1.111111E-01     5.359929E-01     4.444444E+16
250  traj.phases.phase0.indep_states.states:v_26                            c    -1.111111E-01     5.233226E-01     4.444444E+16
251  traj.phases.phase0.indep_states.states:v_27                            c    -1.111111E-01     4.946985E-01     4.444444E+16
252  traj.phases.phase0.indep_states.states:v_28                            c    -1.111111E-01     4.545635E-01     4.444444E+16
253  traj.phases.phase0.indep_states.states:v_29                            c    -1.111111E-01     4.413990E-01     4.444444E+16
254  traj.phases.phase0.indep_states.states:v_30                            c    -1.111111E-01     4.105400E-01     4.444444E+16
255  traj.phases.phase0.indep_states.states:v_31                            c    -1.111111E-01     3.673768E-01     4.444444E+16
256  traj.phases.phase0.indep_states.states:v_32                            c    -1.111111E-01     3.537669E-01     4.444444E+16
257  traj.phases.phase0.indep_states.states:v_33                            c    -1.111111E-01     3.222744E-01     4.444444E+16
258  traj.phases.phase0.indep_states.states:v_34                            c    -1.111111E-01     2.780832E-01     4.444444E+16
259  traj.phases.phase0.indep_states.states:v_35                            c    -1.111111E-01     2.639474E-01     4.444444E+16
260  traj.phases.phase0.indep_states.states:v_36                            c    -1.111111E-01     2.317416E-01     4.444444E+16
261  traj.phases.phase0.indep_states.states:v_37                            c    -1.111111E-01     1.870805E-01     4.444444E+16
262  traj.phases.phase0.indep_states.states:v_38                            c    -1.111111E-01     1.727889E-01     4.444444E+16
263  traj.phases.phase0.indep_states.states:v_39                            c    -1.111111E-01     1.403262E-01     4.444444E+16
264  traj.phases.phase0.indep_states.states:v_40                            c    -1.111111E-01     9.707951E-02     4.444444E+16
265  traj.phases.phase0.indep_states.states:v_41                            c    -1.111111E-01     8.391573E-02     4.444444E+16
266  traj.phases.phase0.indep_states.states:v_42                            c    -1.111111E-01     5.350086E-02     4.444444E+16
267  traj.phases.phase0.indep_states.states:v_43                            c    -1.111111E-01     1.241570E-02     4.444444E+16
268  traj.phases.phase0.control_group.indep_controls.controls:alpha_0       c    -1.570796E+00     3.041688E-01     1.570796E+00
269  traj.phases.phase0.control_group.indep_controls.controls:alpha_1       c    -1.570796E+00     3.051447E-01     1.570796E+00
270  traj.phases.phase0.control_group.indep_controls.controls:alpha_2       c    -1.570796E+00     3.055384E-01     1.570796E+00
271  traj.phases.phase0.control_group.indep_controls.controls:alpha_3       c    -1.570796E+00     3.054327E-01     1.570796E+00
272  traj.phases.phase0.control_group.indep_controls.controls:alpha_4       c    -1.570796E+00     3.046727E-01     1.570796E+00
273  traj.phases.phase0.control_group.indep_controls.controls:alpha_5       c    -1.570796E+00     3.023385E-01     1.570796E+00
274  traj.phases.phase0.control_group.indep_controls.controls:alpha_6       c    -1.570796E+00     3.012892E-01     1.570796E+00
275  traj.phases.phase0.control_group.indep_controls.controls:alpha_7       c    -1.570796E+00     3.000089E-01     1.570796E+00
276  traj.phases.phase0.control_group.indep_controls.controls:alpha_8       c    -1.570796E+00     3.024901E-01     1.570796E+00
277  traj.phases.phase0.control_group.indep_controls.controls:alpha_9       c    -1.570796E+00     3.043015E-01     1.570796E+00
278  traj.phases.phase0.control_group.indep_controls.controls:alpha_10      c    -1.570796E+00     3.074852E-01     1.570796E+00
279  traj.phases.phase0.control_group.indep_controls.controls:alpha_11      c    -1.570796E+00     3.068569E-01     1.570796E+00
280  traj.phases.phase0.control_group.indep_controls.controls:alpha_12      c    -1.570796E+00     3.054450E-01     1.570796E+00
281  traj.phases.phase0.control_group.indep_controls.controls:alpha_13      c    -1.570796E+00     3.026787E-01     1.570796E+00
282  traj.phases.phase0.control_group.indep_controls.controls:alpha_14      c    -1.570796E+00     3.025875E-01     1.570796E+00
283  traj.phases.phase0.control_group.indep_controls.controls:alpha_15      c    -1.570796E+00     3.034586E-01     1.570796E+00
284  traj.phases.phase0.control_group.indep_controls.controls:alpha_16      c    -1.570796E+00     3.051667E-01     1.570796E+00
285  traj.phases.phase0.control_group.indep_controls.controls:alpha_17      c    -1.570796E+00     3.049548E-01     1.570796E+00
286  traj.phases.phase0.control_group.indep_controls.controls:alpha_18      c    -1.570796E+00     3.042672E-01     1.570796E+00
287  traj.phases.phase0.control_group.indep_controls.controls:alpha_19      c    -1.570796E+00     3.031090E-01     1.570796E+00
288  traj.phases.phase0.control_group.indep_controls.controls:alpha_20      c    -1.570796E+00     3.040002E-01     1.570796E+00
289  traj.phases.phase0.control_group.indep_controls.controls:alpha_21      c    -1.570796E+00     3.048836E-01     1.570796E+00
290  traj.phases.phase0.control_group.indep_controls.controls:alpha_22      c    -1.570796E+00     3.062529E-01     1.570796E+00
291  traj.phases.phase0.control_group.indep_controls.controls:alpha_23      c    -1.570796E+00     3.049094E-01     1.570796E+00
292  traj.phases.phase0.control_group.indep_controls.controls:alpha_24      c    -1.570796E+00     3.037032E-01     1.570796E+00
293  traj.phases.phase0.control_group.indep_controls.controls:alpha_25      c    -1.570796E+00     3.016921E-01     1.570796E+00
294  traj.phases.phase0.control_group.indep_controls.controls:alpha_26      c    -1.570796E+00     3.027950E-01     1.570796E+00
295  traj.phases.phase0.control_group.indep_controls.controls:alpha_27      c    -1.570796E+00     3.040809E-01     1.570796E+00
296  traj.phases.phase0.control_group.indep_controls.controls:alpha_28      c    -1.570796E+00     3.064611E-01     1.570796E+00
297  traj.phases.phase0.control_group.indep_controls.controls:alpha_29      c    -1.570796E+00     3.061984E-01     1.570796E+00
298  traj.phases.phase0.control_group.indep_controls.controls:alpha_30      c    -1.570796E+00     3.052584E-01     1.570796E+00
299  traj.phases.phase0.control_group.indep_controls.controls:alpha_31      c    -1.570796E+00     3.032572E-01     1.570796E+00
300  traj.phases.phase0.control_group.indep_controls.controls:alpha_32      c    -1.570796E+00     3.025415E-01     1.570796E+00
301  traj.phases.phase0.control_group.indep_controls.controls:alpha_33      c    -1.570796E+00     3.028092E-01     1.570796E+00
302  traj.phases.phase0.control_group.indep_controls.controls:alpha_34      c    -1.570796E+00     3.034984E-01     1.570796E+00
303  traj.phases.phase0.control_group.indep_controls.controls:alpha_35      c    -1.570796E+00     3.038067E-01     1.570796E+00
304  traj.phases.phase0.control_group.indep_controls.controls:alpha_36      c    -1.570796E+00     3.037490E-01     1.570796E+00
305  traj.phases.phase0.control_group.indep_controls.controls:alpha_37      c    -1.570796E+00     3.040286E-01     1.570796E+00
306  traj.phases.phase0.control_group.indep_controls.controls:alpha_38      c    -1.570796E+00     3.060470E-01     1.570796E+00
307  traj.phases.phase0.control_group.indep_controls.controls:alpha_39      c    -1.570796E+00     3.070802E-01     1.570796E+00
308  traj.phases.phase0.control_group.indep_controls.controls:alpha_40      c    -1.570796E+00     3.073277E-01     1.570796E+00
309  traj.phases.phase0.control_group.indep_controls.controls:alpha_41      c    -1.570796E+00     2.999995E-01     1.570796E+00
310  traj.phases.phase0.control_group.indep_controls.controls:alpha_42      c    -1.570796E+00     2.958273E-01     1.570796E+00
311  traj.phases.phase0.control_group.indep_controls.controls:alpha_43      c    -1.570796E+00     2.875384E-01     1.570796E+00
312  traj.phases.phase0.control_group.indep_controls.controls:alpha_44      c    -1.570796E+00     2.836043E-01     1.570796E+00
313  traj.phases.phase0.control_group.indep_controls.controls:beta_0        c    -1.553343E+00    -1.303263E+00     1.745329E-02
314  traj.phases.phase0.control_group.indep_controls.controls:beta_1        c    -1.553343E+00    -1.275516E+00     1.745329E-02
315  traj.phases.phase0.control_group.indep_controls.controls:beta_2        c    -1.553343E+00    -1.251240E+00     1.745329E-02
316  traj.phases.phase0.control_group.indep_controls.controls:beta_3        c    -1.553343E+00    -1.246941E+00     1.745329E-02
317  traj.phases.phase0.control_group.indep_controls.controls:beta_4        c    -1.553343E+00    -1.239303E+00     1.745329E-02
318  traj.phases.phase0.control_group.indep_controls.controls:beta_5        c    -1.553343E+00    -1.229888E+00     1.745329E-02
319  traj.phases.phase0.control_group.indep_controls.controls:beta_6        c    -1.553343E+00    -1.227180E+00     1.745329E-02
320  traj.phases.phase0.control_group.indep_controls.controls:beta_7        c    -1.553343E+00    -1.209378E+00     1.745329E-02
321  traj.phases.phase0.control_group.indep_controls.controls:beta_8        c    -1.553343E+00    -1.146234E+00     1.745329E-02
322  traj.phases.phase0.control_group.indep_controls.controls:beta_9        c    -1.553343E+00    -1.116929E+00     1.745329E-02
323  traj.phases.phase0.control_group.indep_controls.controls:beta_10       c    -1.553343E+00    -1.057221E+00     1.745329E-02
324  traj.phases.phase0.control_group.indep_controls.controls:beta_11       c    -1.553343E+00    -1.015977E+00     1.745329E-02
325  traj.phases.phase0.control_group.indep_controls.controls:beta_12       c    -1.553343E+00    -1.012862E+00     1.745329E-02
326  traj.phases.phase0.control_group.indep_controls.controls:beta_13       c    -1.553343E+00    -1.003124E+00     1.745329E-02
327  traj.phases.phase0.control_group.indep_controls.controls:beta_14       c    -1.553343E+00    -9.631634E-01     1.745329E-02
328  traj.phases.phase0.control_group.indep_controls.controls:beta_15       c    -1.553343E+00    -9.441083E-01     1.745329E-02
329  traj.phases.phase0.control_group.indep_controls.controls:beta_16       c    -1.553343E+00    -9.009975E-01     1.745329E-02
330  traj.phases.phase0.control_group.indep_controls.controls:beta_17       c    -1.553343E+00    -8.548159E-01     1.745329E-02
331  traj.phases.phase0.control_group.indep_controls.controls:beta_18       c    -1.553343E+00    -8.434132E-01     1.745329E-02
332  traj.phases.phase0.control_group.indep_controls.controls:beta_19       c    -1.553343E+00    -8.164711E-01     1.745329E-02
333  traj.phases.phase0.control_group.indep_controls.controls:beta_20       c    -1.553343E+00    -7.707579E-01     1.745329E-02
334  traj.phases.phase0.control_group.indep_controls.controls:beta_21       c    -1.553343E+00    -7.542270E-01     1.745329E-02
335  traj.phases.phase0.control_group.indep_controls.controls:beta_22       c    -1.553343E+00    -7.180851E-01     1.745329E-02
336  traj.phases.phase0.control_group.indep_controls.controls:beta_23       c    -1.553343E+00    -6.775669E-01     1.745329E-02
337  traj.phases.phase0.control_group.indep_controls.controls:beta_24       c    -1.553343E+00    -6.670018E-01     1.745329E-02
338  traj.phases.phase0.control_group.indep_controls.controls:beta_25       c    -1.553343E+00    -6.407329E-01     1.745329E-02
339  traj.phases.phase0.control_group.indep_controls.controls:beta_26       c    -1.553343E+00    -5.935868E-01     1.745329E-02
340  traj.phases.phase0.control_group.indep_controls.controls:beta_27       c    -1.553343E+00    -5.760319E-01     1.745329E-02
341  traj.phases.phase0.control_group.indep_controls.controls:beta_28       c    -1.553343E+00    -5.375246E-01     1.745329E-02
342  traj.phases.phase0.control_group.indep_controls.controls:beta_29       c    -1.553343E+00    -4.947072E-01     1.745329E-02
343  traj.phases.phase0.control_group.indep_controls.controls:beta_30       c    -1.553343E+00    -4.836475E-01     1.745329E-02
344  traj.phases.phase0.control_group.indep_controls.controls:beta_31       c    -1.553343E+00    -4.577715E-01     1.745329E-02
345  traj.phases.phase0.control_group.indep_controls.controls:beta_32       c    -1.553343E+00    -4.157560E-01     1.745329E-02
346  traj.phases.phase0.control_group.indep_controls.controls:beta_33       c    -1.553343E+00    -4.009333E-01     1.745329E-02
347  traj.phases.phase0.control_group.indep_controls.controls:beta_34       c    -1.553343E+00    -3.668172E-01     1.745329E-02
348  traj.phases.phase0.control_group.indep_controls.controls:beta_35       c    -1.553343E+00    -3.219295E-01     1.745329E-02
349  traj.phases.phase0.control_group.indep_controls.controls:beta_36       c    -1.553343E+00    -3.082507E-01     1.745329E-02
350  traj.phases.phase0.control_group.indep_controls.controls:beta_37       c    -1.553343E+00    -2.775355E-01     1.745329E-02
351  traj.phases.phase0.control_group.indep_controls.controls:beta_38       c    -1.553343E+00    -2.361963E-01     1.745329E-02
352  traj.phases.phase0.control_group.indep_controls.controls:beta_39       c    -1.553343E+00    -2.233642E-01     1.745329E-02
353  traj.phases.phase0.control_group.indep_controls.controls:beta_40       c    -1.553343E+00    -1.938419E-01     1.745329E-02
354  traj.phases.phase0.control_group.indep_controls.controls:beta_41       c    -1.553343E+00    -1.521989E-01     1.745329E-02
355  traj.phases.phase0.control_group.indep_controls.controls:beta_42       c    -1.553343E+00    -1.387996E-01     1.745329E-02
356  traj.phases.phase0.control_group.indep_controls.controls:beta_43       c    -1.553343E+00    -1.026118E-01     1.745329E-02
357  traj.phases.phase0.control_group.indep_controls.controls:beta_44       c    -1.553343E+00    -3.500069E-02     1.745329E-02

Constraints (i - inequality, e - equality)
Index  Name                                                               Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
0  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    5.707889E-14    0.000000E+00              9.00000E+100
1  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.098179E-09    0.000000E+00              9.00000E+100
2  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -5.217402E-09    0.000000E+00              9.00000E+100
3  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -6.742052E-09    0.000000E+00              9.00000E+100
4  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    6.326401E-10    0.000000E+00              9.00000E+100
5  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.874434E-08    0.000000E+00              9.00000E+100
6  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.608095E-08    0.000000E+00              9.00000E+100
7  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    8.396033E-09    0.000000E+00              9.00000E+100
8  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.397932E-08    0.000000E+00              9.00000E+100
9  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.640181E-08    0.000000E+00              9.00000E+100
10  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.008528E-08    0.000000E+00              9.00000E+100
11  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -7.449366E-09    0.000000E+00              9.00000E+100
12  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    5.075722E-09    0.000000E+00              9.00000E+100
13  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    4.701772E-08    0.000000E+00              9.00000E+100
14  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    3.356202E-08    0.000000E+00              9.00000E+100
15  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.152959E-08    0.000000E+00              9.00000E+100
16  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.222467E-08    0.000000E+00              9.00000E+100
17  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.609149E-08    0.000000E+00              9.00000E+100
18  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -8.008612E-09    0.000000E+00              9.00000E+100
19  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.551672E-08    0.000000E+00              9.00000E+100
20  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.092962E-08    0.000000E+00              9.00000E+100
21  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -4.728256E-09    0.000000E+00              9.00000E+100
22  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.958957E-08    0.000000E+00              9.00000E+100
23  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -5.849932E-09    0.000000E+00              9.00000E+100
24  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.141960E-08    0.000000E+00              9.00000E+100
25  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.074738E-08    0.000000E+00              9.00000E+100
26  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -3.343586E-09    0.000000E+00              9.00000E+100
27  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.048372E-08    0.000000E+00              9.00000E+100
28  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    7.662318E-11    0.000000E+00              9.00000E+100
29  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.018746E-08    0.000000E+00              9.00000E+100
30  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.195918E-08    0.000000E+00              9.00000E+100
31  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -9.359846E-09    0.000000E+00              9.00000E+100
32  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -8.609498E-09    0.000000E+00              9.00000E+100
33  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    5.272808E-09    0.000000E+00              9.00000E+100
34  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.683872E-08    0.000000E+00              9.00000E+100
35  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -4.823008E-09    0.000000E+00              9.00000E+100
36  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -9.932651E-09    0.000000E+00              9.00000E+100
37  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    4.066238E-09    0.000000E+00              9.00000E+100
38  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.234618E-08    0.000000E+00              9.00000E+100
39  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    3.537322E-09    0.000000E+00              9.00000E+100
40  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -8.207772E-09    0.000000E+00              9.00000E+100
41  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    3.438402E-09    0.000000E+00              9.00000E+100
42  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.679483E-08    0.000000E+00              9.00000E+100
43  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.005355E-09    0.000000E+00              9.00000E+100
44  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.789710E-09    0.000000E+00              9.00000E+100
45  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    1.210517E-10    0.000000E+00              9.00000E+100
46  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    1.211149E-11    0.000000E+00              9.00000E+100
47  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    2.020261E-13    0.000000E+00              9.00000E+100
48  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    8.856113E-12    0.000000E+00              9.00000E+100
49  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -9.127803E-11    0.000000E+00              9.00000E+100
50  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.241094E-11    0.000000E+00              9.00000E+100
51  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.769883E-10    0.000000E+00              9.00000E+100
52  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -5.289606E-10    0.000000E+00              9.00000E+100
53  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -2.564751E-10    0.000000E+00              9.00000E+100
54  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -4.438898E-11    0.000000E+00              9.00000E+100
55  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    1.914057E-10    0.000000E+00              9.00000E+100
56  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -3.968072E-10    0.000000E+00              9.00000E+100
57  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -4.458924E-10    0.000000E+00              9.00000E+100
58  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -5.118797E-11    0.000000E+00              9.00000E+100
59  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.978903E-10    0.000000E+00              9.00000E+100
60  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -2.365974E-10    0.000000E+00              9.00000E+100
61  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -4.955394E-11    0.000000E+00              9.00000E+100
62  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -9.526139E-11    0.000000E+00              9.00000E+100
63  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.577353E-10    0.000000E+00              9.00000E+100
64  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -4.053666E-11    0.000000E+00              9.00000E+100
65  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -7.273841E-11    0.000000E+00              9.00000E+100
66  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -7.834782E-11    0.000000E+00              9.00000E+100
67  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    2.532058E-11    0.000000E+00              9.00000E+100
68  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -8.237540E-11    0.000000E+00              9.00000E+100
69  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    6.989531E-12    0.000000E+00              9.00000E+100
70  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    1.641027E-10    0.000000E+00              9.00000E+100
71  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    7.985782E-11    0.000000E+00              9.00000E+100
72  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    6.703378E-11    0.000000E+00              9.00000E+100
73  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -7.122201E-11    0.000000E+00              9.00000E+100
74  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    1.754933E-11    0.000000E+00              9.00000E+100
75  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.065551E-10    0.000000E+00              9.00000E+100
76  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -4.820932E-11    0.000000E+00              9.00000E+100
77  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.789572E-10    0.000000E+00              9.00000E+100
78  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.733328E-10    0.000000E+00              9.00000E+100
79  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    9.662116E-12    0.000000E+00              9.00000E+100
80  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -7.118292E-11    0.000000E+00              9.00000E+100
81  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -2.448054E-11    0.000000E+00              9.00000E+100
82  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -8.424070E-11    0.000000E+00              9.00000E+100
83  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    1.295772E-10    0.000000E+00              9.00000E+100
84  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.111705E-10    0.000000E+00              9.00000E+100
85  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    2.320709E-10    0.000000E+00              9.00000E+100
86  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -2.989959E-11    0.000000E+00              9.00000E+100
87  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    4.669378E-10    0.000000E+00              9.00000E+100
88  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    6.122268E-10    0.000000E+00              9.00000E+100
89  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    3.554642E-10    0.000000E+00              9.00000E+100
90  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    2.903182E-17    0.000000E+00              9.00000E+100
91  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    1.580783E-13    0.000000E+00              9.00000E+100
92  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    4.382935E-13    0.000000E+00              9.00000E+100
93  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    4.687914E-13    0.000000E+00              9.00000E+100
94  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    1.076355E-13    0.000000E+00              9.00000E+100
95  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    3.452029E-13    0.000000E+00              9.00000E+100
96  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    6.920026E-13    0.000000E+00              9.00000E+100
97  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    2.093616E-12    0.000000E+00              9.00000E+100
98  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    4.424886E-12    0.000000E+00              9.00000E+100
99  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    4.632594E-12    0.000000E+00              9.00000E+100
100  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    3.184065E-12    0.000000E+00              9.00000E+100
101  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.381045E-13    0.000000E+00              9.00000E+100
102  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -6.057490E-14    0.000000E+00              9.00000E+100
103  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    1.725216E-12    0.000000E+00              9.00000E+100
104  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    7.419809E-13    0.000000E+00              9.00000E+100
105  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.849620E-14    0.000000E+00              9.00000E+100
106  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.628107E-13    0.000000E+00              9.00000E+100
107  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.699813E-13    0.000000E+00              9.00000E+100
108  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -8.985350E-14    0.000000E+00              9.00000E+100
109  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    9.945577E-14    0.000000E+00              9.00000E+100
110  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.411747E-13    0.000000E+00              9.00000E+100
111  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -4.232477E-13    0.000000E+00              9.00000E+100
112  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.706056E-13    0.000000E+00              9.00000E+100
113  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -6.554733E-13    0.000000E+00              9.00000E+100
114  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.000487E-12    0.000000E+00              9.00000E+100
115  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.767399E-12    0.000000E+00              9.00000E+100
116  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.793826E-12    0.000000E+00              9.00000E+100
117  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.513567E-12    0.000000E+00              9.00000E+100
118  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.662551E-12    0.000000E+00              9.00000E+100
119  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.868880E-12    0.000000E+00              9.00000E+100
120  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.710228E-12    0.000000E+00              9.00000E+100
121  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -8.163350E-13    0.000000E+00              9.00000E+100
122  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -5.337065E-13    0.000000E+00              9.00000E+100
123  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -7.799327E-13    0.000000E+00              9.00000E+100
124  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -8.502950E-13    0.000000E+00              9.00000E+100
125  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.433847E-13    0.000000E+00              9.00000E+100
126  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    1.634855E-15    0.000000E+00              9.00000E+100
127  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -6.197387E-14    0.000000E+00              9.00000E+100
128  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -8.491627E-14    0.000000E+00              9.00000E+100
129  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    1.040791E-13    0.000000E+00              9.00000E+100
130  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    5.091039E-13    0.000000E+00              9.00000E+100
131  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    5.437561E-13    0.000000E+00              9.00000E+100
132  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    2.686115E-13    0.000000E+00              9.00000E+100
133  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.427274E-12    0.000000E+00              9.00000E+100
134  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    1.119562E-14    0.000000E+00              9.00000E+100
135  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -8.399696E-13    0.000000E+00              9.00000E+100
136  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    6.237439E-12    0.000000E+00              9.00000E+100
137  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -1.113107E-11    0.000000E+00              9.00000E+100
138  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.573466E-11    0.000000E+00              9.00000E+100
139  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.536226E-11    0.000000E+00              9.00000E+100
140  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.105027E-10    0.000000E+00              9.00000E+100
141  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.839202E-10    0.000000E+00              9.00000E+100
142  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    3.182899E-10    0.000000E+00              9.00000E+100
143  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -4.880937E-11    0.000000E+00              9.00000E+100
144  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -1.000465E-10    0.000000E+00              9.00000E+100
145  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    3.712964E-10    0.000000E+00              9.00000E+100
146  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.799740E-09    0.000000E+00              9.00000E+100
147  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.601595E-09    0.000000E+00              9.00000E+100
148  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.220482E-10    0.000000E+00              9.00000E+100
149  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.680128E-10    0.000000E+00              9.00000E+100
150  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    3.306460E-10    0.000000E+00              9.00000E+100
151  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    7.203861E-11    0.000000E+00              9.00000E+100
152  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.371073E-10    0.000000E+00              9.00000E+100
153  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.301646E-10    0.000000E+00              9.00000E+100
154  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    8.402250E-11    0.000000E+00              9.00000E+100
155  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    4.781356E-11    0.000000E+00              9.00000E+100
156  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    7.545343E-11    0.000000E+00              9.00000E+100
157  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -1.555935E-11    0.000000E+00              9.00000E+100
158  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -4.814480E-11    0.000000E+00              9.00000E+100
159  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -1.006354E-10    0.000000E+00              9.00000E+100
160  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -5.710305E-11    0.000000E+00              9.00000E+100
161  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    7.887088E-11    0.000000E+00              9.00000E+100
162  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -2.211824E-11    0.000000E+00              9.00000E+100
163  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -6.126398E-11    0.000000E+00              9.00000E+100
164  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    3.885301E-11    0.000000E+00              9.00000E+100
165  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.752246E-10    0.000000E+00              9.00000E+100
166  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    7.139768E-11    0.000000E+00              9.00000E+100
167  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.927083E-11    0.000000E+00              9.00000E+100
168  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.058109E-11    0.000000E+00              9.00000E+100
169  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.292797E-11    0.000000E+00              9.00000E+100
170  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    5.240581E-11    0.000000E+00              9.00000E+100
171  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    3.219419E-12    0.000000E+00              9.00000E+100
172  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.349828E-11    0.000000E+00              9.00000E+100
173  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    7.423786E-12    0.000000E+00              9.00000E+100
174  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.419940E-10    0.000000E+00              9.00000E+100
175  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -2.994103E-11    0.000000E+00              9.00000E+100
176  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.453665E-10    0.000000E+00              9.00000E+100
177  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    6.390317E-11    0.000000E+00              9.00000E+100
178  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -5.873873E-10    0.000000E+00              9.00000E+100
179  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.660671E-11    0.000000E+00              9.00000E+100
180  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -1.872483E-19    0.000000E+00              9.00000E+100
181  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -1.933355E-13    0.000000E+00              9.00000E+100
182  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -2.213788E-13    0.000000E+00              9.00000E+100
183  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -1.358984E-13    0.000000E+00              9.00000E+100
184  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    4.844259E-13    0.000000E+00              9.00000E+100
185  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.743916E-12    0.000000E+00              9.00000E+100
186  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.914369E-12    0.000000E+00              9.00000E+100
187  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    2.654109E-12    0.000000E+00              9.00000E+100
188  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    4.445562E-12    0.000000E+00              9.00000E+100
189  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    4.669791E-12    0.000000E+00              9.00000E+100
190  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    3.292695E-12    0.000000E+00              9.00000E+100
191  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    9.306405E-13    0.000000E+00              9.00000E+100
192  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    2.732806E-12    0.000000E+00              9.00000E+100
193  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    9.274347E-12    0.000000E+00              9.00000E+100
194  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    9.955833E-12    0.000000E+00              9.00000E+100
195  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    7.441187E-12    0.000000E+00              9.00000E+100
196  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    4.373430E-12    0.000000E+00              9.00000E+100
197  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    4.031577E-12    0.000000E+00              9.00000E+100
198  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    5.288796E-12    0.000000E+00              9.00000E+100
199  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    8.746323E-12    0.000000E+00              9.00000E+100
200  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    9.596060E-12    0.000000E+00              9.00000E+100
201  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    8.007293E-12    0.000000E+00              9.00000E+100
202  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    6.173944E-12    0.000000E+00              9.00000E+100
203  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    6.674572E-12    0.000000E+00              9.00000E+100
204  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    7.749842E-12    0.000000E+00              9.00000E+100
205  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    7.107713E-12    0.000000E+00              9.00000E+100
206  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    3.324685E-12    0.000000E+00              9.00000E+100
207  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    2.377086E-12    0.000000E+00              9.00000E+100
208  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.819432E-12    0.000000E+00              9.00000E+100
209  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.400978E-12    0.000000E+00              9.00000E+100
210  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    8.185995E-13    0.000000E+00              9.00000E+100
211  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.907427E-13    0.000000E+00              9.00000E+100
212  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -2.177024E-14    0.000000E+00              9.00000E+100
213  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -4.665777E-14    0.000000E+00              9.00000E+100
214  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -9.765943E-14    0.000000E+00              9.00000E+100
215  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -1.752470E-13    0.000000E+00              9.00000E+100
216  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.940777E-14    0.000000E+00              9.00000E+100
217  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -3.367546E-13    0.000000E+00              9.00000E+100
218  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -4.090838E-13    0.000000E+00              9.00000E+100
219  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -4.651370E-13    0.000000E+00              9.00000E+100
220  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    3.340402E-13    0.000000E+00              9.00000E+100
221  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -7.862725E-14    0.000000E+00              9.00000E+100
222  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.836354E-13    0.000000E+00              9.00000E+100
223  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    6.268769E-13    0.000000E+00              9.00000E+100
224  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    2.843691E-12    0.000000E+00              9.00000E+100
225  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.627773E-11    0.000000E+00              9.00000E+100
226  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.630678E-11    0.000000E+00              9.00000E+100
227  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.087714E-12    0.000000E+00              9.00000E+100
228  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    9.180202E-12    0.000000E+00              9.00000E+100
229  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.394420E-11    0.000000E+00              9.00000E+100
230  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    7.320788E-11    0.000000E+00              9.00000E+100
231  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.770419E-10    0.000000E+00              9.00000E+100
232  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.739474E-10    0.000000E+00              9.00000E+100
233  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    8.408745E-11    0.000000E+00              9.00000E+100
234  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.336930E-11    0.000000E+00              9.00000E+100
235  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.750177E-10    0.000000E+00              9.00000E+100
236  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    8.494248E-10    0.000000E+00              9.00000E+100
237  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    7.505366E-10    0.000000E+00              9.00000E+100
238  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.012269E-10    0.000000E+00              9.00000E+100
239  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.664711E-10    0.000000E+00              9.00000E+100
240  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.907272E-10    0.000000E+00              9.00000E+100
241  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.505994E-11    0.000000E+00              9.00000E+100
242  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    7.654806E-11    0.000000E+00              9.00000E+100
243  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.148183E-10    0.000000E+00              9.00000E+100
244  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.063644E-11    0.000000E+00              9.00000E+100
245  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.095124E-11    0.000000E+00              9.00000E+100
246  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.126405E-11    0.000000E+00              9.00000E+100
247  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.634971E-12    0.000000E+00              9.00000E+100
248  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.667540E-11    0.000000E+00              9.00000E+100
249  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.184178E-11    0.000000E+00              9.00000E+100
250  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.030586E-12    0.000000E+00              9.00000E+100
251  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.233150E-11    0.000000E+00              9.00000E+100
252  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.607544E-12    0.000000E+00              9.00000E+100
253  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.309422E-11    0.000000E+00              9.00000E+100
254  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    9.246994E-12    0.000000E+00              9.00000E+100
255  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.950662E-11    0.000000E+00              9.00000E+100
256  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.410942E-11    0.000000E+00              9.00000E+100
257  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.798072E-11    0.000000E+00              9.00000E+100
258  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.156640E-11    0.000000E+00              9.00000E+100
259  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.330623E-12    0.000000E+00              9.00000E+100
260  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.982138E-11    0.000000E+00              9.00000E+100
261  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    7.408593E-12    0.000000E+00              9.00000E+100
262  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.187812E-11    0.000000E+00              9.00000E+100
263  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.754402E-11    0.000000E+00              9.00000E+100
264  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.677139E-11    0.000000E+00              9.00000E+100
265  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -5.399948E-13    0.000000E+00              9.00000E+100
266  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.582294E-11    0.000000E+00              9.00000E+100
267  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -8.825067E-12    0.000000E+00              9.00000E+100
268  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.129888E-11    0.000000E+00              9.00000E+100
269  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.039670E-12    0.000000E+00              9.00000E+100
270  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    4.162551E-15    0.000000E+00              9.00000E+100
271  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    2.544821E-15    0.000000E+00              9.00000E+100
272  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    9.117807E-16    0.000000E+00              9.00000E+100
273  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -8.437374E-16    0.000000E+00              9.00000E+100
274  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    7.893027E-16    0.000000E+00              9.00000E+100
275  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -2.531212E-15    0.000000E+00              9.00000E+100
276  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    8.301287E-16    0.000000E+00              9.00000E+100
277  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -8.301287E-16    0.000000E+00              9.00000E+100
278  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -4.164252E-15    0.000000E+00              9.00000E+100
279  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -6.661443E-15    0.000000E+00              9.00000E+100
280  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -2.531212E-15    0.000000E+00              9.00000E+100
281  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    4.155747E-15    0.000000E+00              9.00000E+100
282  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    4.164252E-15    0.000000E+00              9.00000E+100
283  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    8.165201E-16    0.000000E+00              9.00000E+100
284  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00   -3.320515E-15    0.000000E+00              9.00000E+100
285  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00   -1.009763E-14    0.000000E+00              9.00000E+100
286  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00   -8.491809E-15    0.000000E+00              9.00000E+100
287  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00   -3.327319E-15    0.000000E+00              9.00000E+100
288  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    9.145025E-15    0.000000E+00              9.00000E+100
289  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    4.354774E-16    0.000000E+00              9.00000E+100
290  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    1.001598E-14    0.000000E+00              9.00000E+100
291  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    6.695465E-15    0.000000E+00              9.00000E+100
292  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    6.641030E-15    0.000000E+00              9.00000E+100
293  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
294  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00   -2.830603E-15    0.000000E+00              9.00000E+100
295  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    1.088693E-15    0.000000E+00              9.00000E+100
296  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00   -8.709547E-16    0.000000E+00              9.00000E+100
297  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    7.620854E-16    0.000000E+00              9.00000E+100
298  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    5.551115E-17    0.000000E+00              9.00000E+100
299  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    5.551115E-17    0.000000E+00              9.00000E+100
300  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
301  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    5.551115E-17    0.000000E+00              9.00000E+100
302  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    5.551115E-17    0.000000E+00              9.00000E+100
303  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00   -5.551115E-17    0.000000E+00              9.00000E+100
304  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00   -5.551115E-17    0.000000E+00              9.00000E+100
305  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    5.551115E-17    0.000000E+00              9.00000E+100
306  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
307  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    5.551115E-17    0.000000E+00              9.00000E+100
308  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
309  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00   -5.551115E-17    0.000000E+00              9.00000E+100
310  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    5.551115E-17    0.000000E+00              9.00000E+100
311  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    5.551115E-17    0.000000E+00              9.00000E+100
312  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
313  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
314  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    4.440892E-16    0.000000E+00              9.00000E+100
315  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
316  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00   -2.220446E-16    0.000000E+00              9.00000E+100
317  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    3.330669E-16    0.000000E+00              9.00000E+100
318  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    1.110223E-16    0.000000E+00              9.00000E+100
319  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    3.330669E-16    0.000000E+00              9.00000E+100
320  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
321  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
322  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
323  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
324  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    2.775558E-17    0.000000E+00              9.00000E+100
325  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00   -5.551115E-17    0.000000E+00              9.00000E+100

Exit Status
Inform  Description
0  Optimization terminated successfully.
--------------------------------------------------------------------------------

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

Done simulating trajectory traj

False

sol = om.CaseReader('dymos_solution.db').get_case('final')

plot_results([('traj.phase0.timeseries.time', 'traj.phase0.timeseries.alpha',
('traj.phase0.timeseries.time', 'traj.phase0.timeseries.beta',
('traj.phase0.timeseries.time', 'traj.phase0.timeseries.theta',