SSTO Lunar Ascent with Polynomial Controls#

This example demonstrates the use of polynomial controls in Dymos. Polynomial controls define the control profile as a single polynomial across the entire phase where the control values are specified at the Legendre Gauss Lobatto (LGL) nodes in phase dimensionless time. These controls can be of any arbitrary order greater than 1 (linear).

We’ve already demonstrated that the optimal single stage ascent in the absense of an atmosphere follows the linear tangent guidance law. In this example, we’ll change the control parameterization such that \(\tan \theta\) is provided by a polynomial control of order 1. The LGL nodes of a first order polynomial are the endpoints of the phase, thus the optimizer will be governing the value of \(\tan \theta\) at the initial and final times of the phase, and the Dymos will interpolate the values of \(\tan \theta\) to all other nodes in the Phase.

This example is equivalent to the previous linear tangent example in that we’ve reduced the problem from finding the appropriate control value at all nodes to that of finding the optimal value of just two quantities. But instead of optimizing the slope and intercept given by the parameters \(a\) and \(b\), we’re parameterizing the control using the endpoint values of the linear polynomial.

Now the guidance comp needs to convert the inverse tangent of the current value of the polynomial controls.

\[\theta = \arctan{p}\]

Solving the problem#

import numpy as np
import matplotlib.pyplot as plt
import openmdao.api as om
import dymos as dm

g = 1.61544  # lunar gravity, m/s**2

class LaunchVehicle2DEOM(om.ExplicitComponent):
    """
    Simple 2D Cartesian Equations of Motion for a launch vehicle subject to thrust and drag.
    """
    def initialize(self):
        self.options.declare('num_nodes', types=int)

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

        # Inputs
        self.add_input('vx',
                       val=np.zeros(nn),
                       desc='x velocity',
                       units='m/s')

        self.add_input('vy',
                       val=np.zeros(nn),
                       desc='y velocity',
                       units='m/s')

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

        self.add_input('theta',
                       val=np.zeros(nn),
                       desc='pitch angle',
                       units='rad')

        self.add_input('thrust',
                       val=2100000 * np.ones(nn),
                       desc='thrust',
                       units='N')

        self.add_input('Isp',
                       val=265.2 * np.ones(nn),
                       desc='specific impulse',
                       units='s')

        # Outputs
        self.add_output('xdot',
                        val=np.zeros(nn),
                        desc='velocity component in x',
                        units='m/s')

        self.add_output('ydot',
                        val=np.zeros(nn),
                        desc='velocity component in y',
                        units='m/s')

        self.add_output('vxdot',
                        val=np.zeros(nn),
                        desc='x acceleration magnitude',
                        units='m/s**2')

        self.add_output('vydot',
                        val=np.zeros(nn),
                        desc='y acceleration magnitude',
                        units='m/s**2')

        self.add_output('mdot',
                        val=np.zeros(nn),
                        desc='mass rate of change',
                        units='kg/s')

        # Setup partials
        ar = np.arange(self.options['num_nodes'])

        self.declare_partials(of='xdot', wrt='vx', rows=ar, cols=ar, val=1.0)
        self.declare_partials(of='ydot', wrt='vy', rows=ar, cols=ar, val=1.0)

        self.declare_partials(of='vxdot', wrt='vx', rows=ar, cols=ar)
        self.declare_partials(of='vxdot', wrt='m', rows=ar, cols=ar)
        self.declare_partials(of='vxdot', wrt='theta', rows=ar, cols=ar)
        self.declare_partials(of='vxdot', wrt='thrust', rows=ar, cols=ar)

        self.declare_partials(of='vydot', wrt='m', rows=ar, cols=ar)
        self.declare_partials(of='vydot', wrt='theta', rows=ar, cols=ar)
        self.declare_partials(of='vydot', wrt='vy', rows=ar, cols=ar)
        self.declare_partials(of='vydot', wrt='thrust', rows=ar, cols=ar)

        self.declare_partials(of='mdot', wrt='thrust', rows=ar, cols=ar)
        self.declare_partials(of='mdot', wrt='Isp', rows=ar, cols=ar)

    def compute(self, inputs, outputs):
        theta = inputs['theta']
        cos_theta = np.cos(theta)
        sin_theta = np.sin(theta)
        vx = inputs['vx']
        vy = inputs['vy']
        m = inputs['m']
        F_T = inputs['thrust']
        Isp = inputs['Isp']

        outputs['xdot'] = vx
        outputs['ydot'] = vy
        outputs['vxdot'] = F_T * cos_theta / m
        outputs['vydot'] = F_T * sin_theta / m - g
        outputs['mdot'] = -F_T / (g * Isp)

    def compute_partials(self, inputs, jacobian):
        theta = inputs['theta']
        cos_theta = np.cos(theta)
        sin_theta = np.sin(theta)
        m = inputs['m']
        F_T = inputs['thrust']
        Isp = inputs['Isp']

        # jacobian['vxdot', 'vx'] = -CDA * rho * vx / m
        jacobian['vxdot', 'm'] = -(F_T * cos_theta) / m ** 2
        jacobian['vxdot', 'theta'] = -(F_T / m) * sin_theta
        jacobian['vxdot', 'thrust'] = cos_theta / m

        # jacobian['vydot', 'vy'] = -CDA * rho * vy / m
        jacobian['vydot', 'm'] = -(F_T * sin_theta) / m ** 2
        jacobian['vydot', 'theta'] = (F_T / m) * cos_theta
        jacobian['vydot', 'thrust'] = sin_theta / m

        jacobian['mdot', 'thrust'] = -1.0 / (g * Isp)
        jacobian['mdot', 'Isp'] = F_T / (g * Isp ** 2)

class LaunchVehicleLinearTangentODE(om.Group):
    """
    The LaunchVehicleLinearTangentODE for this case consists of a guidance component and
    the EOM.  Guidance is simply an OpenMDAO ExecComp which computes the arctangent of the
    tan_theta variable.
    """

    def initialize(self):
        self.options.declare('num_nodes', types=int,
                             desc='Number of nodes to be evaluated in the RHS')

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

        self.add_subsystem('guidance', om.ExecComp('theta=arctan(tan_theta)',
                                                   theta={'val': np.ones(nn),
                                                          'units': 'rad'},
                                                   tan_theta={'val': np.ones(nn)}))

        self.add_subsystem('eom', LaunchVehicle2DEOM(num_nodes=nn))

        self.connect('guidance.theta', 'eom.theta')

#
# Setup and solve the optimal control problem
#
p = om.Problem(model=om.Group())

traj = p.model.add_subsystem('traj', dm.Trajectory())

phase = dm.Phase(ode_class=LaunchVehicleLinearTangentODE,
                 transcription=dm.Radau(num_segments=20, order=3, compressed=False))
traj.add_phase('phase0', phase)

phase.set_time_options(fix_initial=True, duration_bounds=(10, 1000), units='s')

#
# Set the state options.  We include rate_source, units, and targets here since the ODE
# is not decorated with their default values.
#
phase.add_state('x', fix_initial=True, lower=0, rate_source='eom.xdot', units='m')
phase.add_state('y', fix_initial=True, lower=0, rate_source='eom.ydot', units='m')
phase.add_state('vx', fix_initial=True, lower=0, rate_source='eom.vxdot',
                units='m/s', targets=['eom.vx'])
phase.add_state('vy', fix_initial=True, rate_source='eom.vydot',
                units='m/s', targets=['eom.vy'])
phase.add_state('m', fix_initial=True, rate_source='eom.mdot',
                units='kg', targets=['eom.m'])

#
# The tangent of theta is modeled as a linear polynomial over the duration of the phase.
#
phase.add_polynomial_control('tan_theta', order=1, units=None, opt=True,
                             targets=['guidance.tan_theta'])

#
# Parameters values for thrust and specific impulse are design parameters. They are
# provided by an IndepVarComp in the phase, but with opt=False their values are not
# design variables in the optimization problem.
#
phase.add_parameter('thrust', units='N', opt=False, val=3.0 * 50000.0 * 1.61544,
                    targets=['eom.thrust'])
phase.add_parameter('Isp', units='s', opt=False, val=1.0E6, targets=['eom.Isp'])

#
# Set the boundary constraints.  These are all states which could also be handled
# by setting fix_final=True and including the correct final value in the initial guess.
#
phase.add_boundary_constraint('y', loc='final', equals=1.85E5, linear=True)
phase.add_boundary_constraint('vx', loc='final', equals=1627.0)
phase.add_boundary_constraint('vy', loc='final', equals=0)

phase.add_objective('time', index=-1, scaler=0.01)

#
# Add theta as a timeseries output since it's not included by default.
#
phase.add_timeseries_output('guidance.theta', units='deg')

#
# Set the optimizer
#
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'SLSQP'
p.driver.declare_coloring()

#
# We don't strictly need to define a linear solver here since our problem is entirely
# feed-forward with no iterative loops.  It's good practice to add one, however, since
# failing to do so can cause incorrect derivatives if iterative processes are ever
# introduced to the system.
#
p.model.linear_solver = om.DirectSolver()

p.setup(check=True)

#
# Assign initial guesses for the independent variables in the problem.
#
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 500.0
p['traj.phase0.states:x'] = phase.interp('x', [0, 350000.0])
p['traj.phase0.states:y'] = phase.interp('y', [0, 185000.0])
p['traj.phase0.states:vx'] = phase.interp('vx', [0, 1627.0])
p['traj.phase0.states:vy'] = phase.interp('vy', [1.0E-6, 0])
p['traj.phase0.states:m'] = phase.interp('m', [50000, 50000])
p['traj.phase0.polynomial_controls:tan_theta'] = [[0.5 * np.pi], [0.0]]

#
# Solve the problem.
#
dm.run_problem(p, simulate=True)
--- Constraint Report [traj] ---
    --- phase0 ---
        [final]   1.8500e+05 == y [m]
        [final]   1.6270e+03 == vx [m/s]
        [final]   0.0000e+00 == vy [m/s]

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
Coloring for 'traj.phases.phase0.rhs_all.guidance' (class ExecComp)

Jacobian shape: (80, 80)  ( 1.25% nonzero)
FWD solves: 1   REV solves: 0
Total colors vs. total size: 1 vs 80  (98.8% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.004738 sec.
Time to compute coloring: 0.009431 sec.
Memory to compute coloring: 0.421875 MB.
Full total jacobian was computed 3 times, taking 0.256014 seconds.
Total jacobian shape: (303, 398) 
Jacobian shape: (303, 398)  ( 1.74% nonzero)
FWD solves: 11   REV solves: 0
Total colors vs. total size: 11 vs 398  (97.2% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.256014 sec.
Time to compute coloring: 0.356721 sec.
Memory to compute coloring: 1.300781 MB.
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
    Objective Function: _objfunc

    Solution: 
--------------------------------------------------------------------------------
    Total Time:                    1.3762
       User Objective Time :       0.0127
       User Sensitivity Time :     0.0553
       Interface Time :            0.1040
       Opt Solver Time:            1.2042
    Calls to Objective Function :       6
    Calls to Sens Function :            5


   Objectives
      Index  Name                                 Value
          0  traj.phases.phase0.time.t     4.817168E+00

   Variables (c - continuous, i - integer, d - discrete)
      Index  Name                                                                                                    Type      Lower Bound            Value      Upper Bound     Status
          0  traj.phases.phase0.time_extents.t_duration_0                                                               c     1.000000E+01     4.817168E+02     1.000000E+03           
          1  traj.phases.phase0.indep_states.states:x_0                                                                 c     0.000000E+00     6.106930E+01     1.000000E+21           
          2  traj.phases.phase0.indep_states.states:x_1                                                                 c     0.000000E+00     3.496393E+02     1.000000E+21           
          3  traj.phases.phase0.indep_states.states:x_2                                                                 c     0.000000E+00     4.914075E+02     1.000000E+21           
          4  traj.phases.phase0.indep_states.states:x_3                                                                 c     0.000000E+00     4.914075E+02     1.000000E+21           
          5  traj.phases.phase0.indep_states.states:x_4                                                                 c     0.000000E+00     9.095034E+02     1.000000E+21           
          6  traj.phases.phase0.indep_states.states:x_5                                                                 c     0.000000E+00     1.704975E+03     1.000000E+21           
          7  traj.phases.phase0.indep_states.states:x_6                                                                 c     0.000000E+00     2.010769E+03     1.000000E+21           
          8  traj.phases.phase0.indep_states.states:x_7                                                                 c     0.000000E+00     2.010769E+03     1.000000E+21           
          9  traj.phases.phase0.indep_states.states:x_8                                                                 c     0.000000E+00     2.811263E+03     1.000000E+21           
         10  traj.phases.phase0.indep_states.states:x_9                                                                 c     0.000000E+00     4.150586E+03     1.000000E+21           
         11  traj.phases.phase0.indep_states.states:x_10                                                                c     0.000000E+00     4.632596E+03     1.000000E+21           
         12  traj.phases.phase0.indep_states.states:x_11                                                                c     0.000000E+00     4.632596E+03     1.000000E+21           
         13  traj.phases.phase0.indep_states.states:x_12                                                                c     0.000000E+00     5.844355E+03     1.000000E+21           
         14  traj.phases.phase0.indep_states.states:x_13                                                                c     0.000000E+00     7.769668E+03     1.000000E+21           
         15  traj.phases.phase0.indep_states.states:x_14                                                                c     0.000000E+00     8.441819E+03     1.000000E+21           
         16  traj.phases.phase0.indep_states.states:x_15                                                                c     0.000000E+00     8.441819E+03     1.000000E+21           
         17  traj.phases.phase0.indep_states.states:x_16                                                                c     0.000000E+00     1.009787E+04     1.000000E+21           
         18  traj.phases.phase0.indep_states.states:x_17                                                                c     0.000000E+00     1.265747E+04     1.000000E+21           
         19  traj.phases.phase0.indep_states.states:x_18                                                                c     0.000000E+00     1.353576E+04     1.000000E+21           
         20  traj.phases.phase0.indep_states.states:x_19                                                                c     0.000000E+00     1.353576E+04     1.000000E+21           
         21  traj.phases.phase0.indep_states.states:x_20                                                                c     0.000000E+00     1.567405E+04     1.000000E+21           
         22  traj.phases.phase0.indep_states.states:x_21                                                                c     0.000000E+00     1.892357E+04     1.000000E+21           
         23  traj.phases.phase0.indep_states.states:x_22                                                                c     0.000000E+00     2.002641E+04     1.000000E+21           
         24  traj.phases.phase0.indep_states.states:x_23                                                                c     0.000000E+00     2.002641E+04     1.000000E+21           
         25  traj.phases.phase0.indep_states.states:x_24                                                                c     0.000000E+00     2.269073E+04     1.000000E+21           
         26  traj.phases.phase0.indep_states.states:x_25                                                                c     0.000000E+00     2.669437E+04     1.000000E+21           
         27  traj.phases.phase0.indep_states.states:x_26                                                                c     0.000000E+00     2.804305E+04     1.000000E+21           
         28  traj.phases.phase0.indep_states.states:x_27                                                                c     0.000000E+00     2.804305E+04     1.000000E+21           
         29  traj.phases.phase0.indep_states.states:x_28                                                                c     0.000000E+00     3.128395E+04     1.000000E+21           
         30  traj.phases.phase0.indep_states.states:x_29                                                                c     0.000000E+00     3.611577E+04     1.000000E+21           
         31  traj.phases.phase0.indep_states.states:x_30                                                                c     0.000000E+00     3.773482E+04     1.000000E+21           
         32  traj.phases.phase0.indep_states.states:x_31                                                                c     0.000000E+00     3.773482E+04     1.000000E+21           
         33  traj.phases.phase0.indep_states.states:x_32                                                                c     0.000000E+00     4.161043E+04     1.000000E+21           
         34  traj.phases.phase0.indep_states.states:x_33                                                                c     0.000000E+00     4.735527E+04     1.000000E+21           
         35  traj.phases.phase0.indep_states.states:x_34                                                                c     0.000000E+00     4.927265E+04     1.000000E+21           
         36  traj.phases.phase0.indep_states.states:x_35                                                                c     0.000000E+00     4.927265E+04     1.000000E+21           
         37  traj.phases.phase0.indep_states.states:x_36                                                                c     0.000000E+00     5.384901E+04     1.000000E+21           
         38  traj.phases.phase0.indep_states.states:x_37                                                                c     0.000000E+00     6.060228E+04     1.000000E+21           
         39  traj.phases.phase0.indep_states.states:x_38                                                                c     0.000000E+00     6.284916E+04     1.000000E+21           
         40  traj.phases.phase0.indep_states.states:x_39                                                                c     0.000000E+00     6.284916E+04     1.000000E+21           
         41  traj.phases.phase0.indep_states.states:x_40                                                                c     0.000000E+00     6.819918E+04     1.000000E+21           
         42  traj.phases.phase0.indep_states.states:x_41                                                                c     0.000000E+00     7.606414E+04     1.000000E+21           
         43  traj.phases.phase0.indep_states.states:x_42                                                                c     0.000000E+00     7.867365E+04     1.000000E+21           
         44  traj.phases.phase0.indep_states.states:x_43                                                                c     0.000000E+00     7.867365E+04     1.000000E+21           
         45  traj.phases.phase0.indep_states.states:x_44                                                                c     0.000000E+00     8.487336E+04     1.000000E+21           
         46  traj.phases.phase0.indep_states.states:x_45                                                                c     0.000000E+00     9.395375E+04     1.000000E+21           
         47  traj.phases.phase0.indep_states.states:x_46                                                                c     0.000000E+00     9.695801E+04     1.000000E+21           
         48  traj.phases.phase0.indep_states.states:x_47                                                                c     0.000000E+00     9.695801E+04     1.000000E+21           
         49  traj.phases.phase0.indep_states.states:x_48                                                                c     0.000000E+00     1.040786E+05     1.000000E+21           
         50  traj.phases.phase0.indep_states.states:x_49                                                                c     0.000000E+00     1.144647E+05     1.000000E+21           
         51  traj.phases.phase0.indep_states.states:x_50                                                                c     0.000000E+00     1.178897E+05     1.000000E+21           
         52  traj.phases.phase0.indep_states.states:x_51                                                                c     0.000000E+00     1.178897E+05     1.000000E+21           
         53  traj.phases.phase0.indep_states.states:x_52                                                                c     0.000000E+00     1.259848E+05     1.000000E+21           
         54  traj.phases.phase0.indep_states.states:x_53                                                                c     0.000000E+00     1.377346E+05     1.000000E+21           
         55  traj.phases.phase0.indep_states.states:x_54                                                                c     0.000000E+00     1.415942E+05     1.000000E+21           
         56  traj.phases.phase0.indep_states.states:x_55                                                                c     0.000000E+00     1.415942E+05     1.000000E+21           
         57  traj.phases.phase0.indep_states.states:x_56                                                                c     0.000000E+00     1.506865E+05     1.000000E+21           
         58  traj.phases.phase0.indep_states.states:x_57                                                                c     0.000000E+00     1.638094E+05     1.000000E+21           
         59  traj.phases.phase0.indep_states.states:x_58                                                                c     0.000000E+00     1.681011E+05     1.000000E+21           
         60  traj.phases.phase0.indep_states.states:x_59                                                                c     0.000000E+00     1.681011E+05     1.000000E+21           
         61  traj.phases.phase0.indep_states.states:x_60                                                                c     0.000000E+00     1.781752E+05     1.000000E+21           
         62  traj.phases.phase0.indep_states.states:x_61                                                                c     0.000000E+00     1.926292E+05     1.000000E+21           
         63  traj.phases.phase0.indep_states.states:x_62                                                                c     0.000000E+00     1.973350E+05     1.000000E+21           
         64  traj.phases.phase0.indep_states.states:x_63                                                                c     0.000000E+00     1.973350E+05     1.000000E+21           
         65  traj.phases.phase0.indep_states.states:x_64                                                                c     0.000000E+00     2.083426E+05     1.000000E+21           
         66  traj.phases.phase0.indep_states.states:x_65                                                                c     0.000000E+00     2.240467E+05     1.000000E+21           
         67  traj.phases.phase0.indep_states.states:x_66                                                                c     0.000000E+00     2.291382E+05     1.000000E+21           
         68  traj.phases.phase0.indep_states.states:x_67                                                                c     0.000000E+00     2.291382E+05     1.000000E+21           
         69  traj.phases.phase0.indep_states.states:x_68                                                                c     0.000000E+00     2.410104E+05     1.000000E+21           
         70  traj.phases.phase0.indep_states.states:x_69                                                                c     0.000000E+00     2.578637E+05     1.000000E+21           
         71  traj.phases.phase0.indep_states.states:x_70                                                                c     0.000000E+00     2.633083E+05     1.000000E+21           
         72  traj.phases.phase0.indep_states.states:x_71                                                                c     0.000000E+00     2.633083E+05     1.000000E+21           
         73  traj.phases.phase0.indep_states.states:x_72                                                                c     0.000000E+00     2.759693E+05     1.000000E+21           
         74  traj.phases.phase0.indep_states.states:x_73                                                                c     0.000000E+00     2.938674E+05     1.000000E+21           
         75  traj.phases.phase0.indep_states.states:x_74                                                                c     0.000000E+00     2.996321E+05     1.000000E+21           
         76  traj.phases.phase0.indep_states.states:x_75                                                                c     0.000000E+00     2.996321E+05     1.000000E+21           
         77  traj.phases.phase0.indep_states.states:x_76                                                                c     0.000000E+00     3.130082E+05     1.000000E+21           
         78  traj.phases.phase0.indep_states.states:x_77                                                                c     0.000000E+00     3.318524E+05     1.000000E+21           
         79  traj.phases.phase0.indep_states.states:x_78                                                                c     0.000000E+00     3.379071E+05     1.000000E+21           
         80  traj.phases.phase0.indep_states.states:y_0                                                                 c     0.000000E+00     1.072874E+02     1.000000E+21           
         81  traj.phases.phase0.indep_states.states:y_1                                                                 c     0.000000E+00     6.062100E+02     1.000000E+21           
         82  traj.phases.phase0.indep_states.states:y_2                                                                 c     0.000000E+00     8.484836E+02     1.000000E+21           
         83  traj.phases.phase0.indep_states.states:y_3                                                                 c     0.000000E+00     8.484836E+02     1.000000E+21           
         84  traj.phases.phase0.indep_states.states:y_4                                                                 c     0.000000E+00     1.555240E+03     1.000000E+21           
         85  traj.phases.phase0.indep_states.states:y_5                                                                 c     0.000000E+00     2.875780E+03     1.000000E+21           
         86  traj.phases.phase0.indep_states.states:y_6                                                                 c     0.000000E+00     3.376666E+03     1.000000E+21           
         87  traj.phases.phase0.indep_states.states:y_7                                                                 c     0.000000E+00     3.376666E+03     1.000000E+21           
         88  traj.phases.phase0.indep_states.states:y_8                                                                 c     0.000000E+00     4.672843E+03     1.000000E+21           
         89  traj.phases.phase0.indep_states.states:y_9                                                                 c     0.000000E+00     6.799841E+03     1.000000E+21           
         90  traj.phases.phase0.indep_states.states:y_10                                                                c     0.000000E+00     7.554202E+03     1.000000E+21           
         91  traj.phases.phase0.indep_states.states:y_11                                                                c     0.000000E+00     7.554202E+03     1.000000E+21           
         92  traj.phases.phase0.indep_states.states:y_12                                                                c     0.000000E+00     9.427357E+03     1.000000E+21           
         93  traj.phases.phase0.indep_states.states:y_13                                                                c     0.000000E+00     1.234194E+04     1.000000E+21           
         94  traj.phases.phase0.indep_states.states:y_14                                                                c     0.000000E+00     1.334336E+04     1.000000E+21           
         95  traj.phases.phase0.indep_states.states:y_15                                                                c     0.000000E+00     1.334336E+04     1.000000E+21           
         96  traj.phases.phase0.indep_states.states:y_16                                                                c     0.000000E+00     1.577789E+04     1.000000E+21           
         97  traj.phases.phase0.indep_states.states:y_17                                                                c     0.000000E+00     1.945627E+04     1.000000E+21           
         98  traj.phases.phase0.indep_states.states:y_18                                                                c     0.000000E+00     2.069660E+04     1.000000E+21           
         99  traj.phases.phase0.indep_states.states:y_19                                                                c     0.000000E+00     2.069660E+04     1.000000E+21           
        100  traj.phases.phase0.indep_states.states:y_20                                                                c     0.000000E+00     2.367267E+04     1.000000E+21           
        101  traj.phases.phase0.indep_states.states:y_21                                                                c     0.000000E+00     2.808440E+04     1.000000E+21           
        102  traj.phases.phase0.indep_states.states:y_22                                                                c     0.000000E+00     2.955320E+04     1.000000E+21           
        103  traj.phases.phase0.indep_states.states:y_23                                                                c     0.000000E+00     2.955320E+04     1.000000E+21           
        104  traj.phases.phase0.indep_states.states:y_24                                                                c     0.000000E+00     3.304522E+04     1.000000E+21           
        105  traj.phases.phase0.indep_states.states:y_25                                                                c     0.000000E+00     3.815080E+04     1.000000E+21           
        106  traj.phases.phase0.indep_states.states:y_26                                                                c     0.000000E+00     3.983445E+04     1.000000E+21           
        107  traj.phases.phase0.indep_states.states:y_27                                                                c     0.000000E+00     3.983445E+04     1.000000E+21           
        108  traj.phases.phase0.indep_states.states:y_28                                                                c     0.000000E+00     4.380893E+04     1.000000E+21           
        109  traj.phases.phase0.indep_states.states:y_29                                                                c     0.000000E+00     4.955634E+04     1.000000E+21           
        110  traj.phases.phase0.indep_states.states:y_30                                                                c     0.000000E+00     5.143680E+04     1.000000E+21           
        111  traj.phases.phase0.indep_states.states:y_31                                                                c     0.000000E+00     5.143680E+04     1.000000E+21           
        112  traj.phases.phase0.indep_states.states:y_32                                                                c     0.000000E+00     5.584932E+04     1.000000E+21           
        113  traj.phases.phase0.indep_states.states:y_33                                                                c     0.000000E+00     6.216918E+04     1.000000E+21           
        114  traj.phases.phase0.indep_states.states:y_34                                                                c     0.000000E+00     6.422234E+04     1.000000E+21           
        115  traj.phases.phase0.indep_states.states:y_35                                                                c     0.000000E+00     6.422234E+04     1.000000E+21           
        116  traj.phases.phase0.indep_states.states:y_36                                                                c     0.000000E+00     6.901329E+04     1.000000E+21           
        117  traj.phases.phase0.indep_states.states:y_37                                                                c     0.000000E+00     7.581228E+04     1.000000E+21           
        118  traj.phases.phase0.indep_states.states:y_38                                                                c     0.000000E+00     7.800565E+04     1.000000E+21           
        119  traj.phases.phase0.indep_states.states:y_39                                                                c     0.000000E+00     7.800565E+04     1.000000E+21           
        120  traj.phases.phase0.indep_states.states:y_40                                                                c     0.000000E+00     8.309475E+04     1.000000E+21           
        121  traj.phases.phase0.indep_states.states:y_41                                                                c     0.000000E+00     9.024734E+04     1.000000E+21           
        122  traj.phases.phase0.indep_states.states:y_42                                                                c     0.000000E+00     9.253734E+04     1.000000E+21           
        123  traj.phases.phase0.indep_states.states:y_43                                                                c     0.000000E+00     9.253734E+04     1.000000E+21           
        124  traj.phases.phase0.indep_states.states:y_44                                                                c     0.000000E+00     9.781724E+04     1.000000E+21           
        125  traj.phases.phase0.indep_states.states:y_45                                                                c     0.000000E+00     1.051572E+05     1.000000E+21           
        126  traj.phases.phase0.indep_states.states:y_46                                                                c     0.000000E+00     1.074866E+05     1.000000E+21           
        127  traj.phases.phase0.indep_states.states:y_47                                                                c     0.000000E+00     1.074866E+05     1.000000E+21           
        128  traj.phases.phase0.indep_states.states:y_48                                                                c     0.000000E+00     1.128178E+05     1.000000E+21           
        129  traj.phases.phase0.indep_states.states:y_49                                                                c     0.000000E+00     1.201334E+05     1.000000E+21           
        130  traj.phases.phase0.indep_states.states:y_50                                                                c     0.000000E+00     1.224307E+05     1.000000E+21           
        131  traj.phases.phase0.indep_states.states:y_51                                                                c     0.000000E+00     1.224307E+05     1.000000E+21           
        132  traj.phases.phase0.indep_states.states:y_52                                                                c     0.000000E+00     1.276417E+05     1.000000E+21           
        133  traj.phases.phase0.indep_states.states:y_53                                                                c     0.000000E+00     1.346812E+05     1.000000E+21           
        134  traj.phases.phase0.indep_states.states:y_54                                                                c     0.000000E+00     1.368636E+05     1.000000E+21           
        135  traj.phases.phase0.indep_states.states:y_55                                                                c     0.000000E+00     1.368636E+05     1.000000E+21           
        136  traj.phases.phase0.indep_states.states:y_56                                                                c     0.000000E+00     1.417612E+05     1.000000E+21           
        137  traj.phases.phase0.indep_states.states:y_57                                                                c     0.000000E+00     1.482532E+05     1.000000E+21           
        138  traj.phases.phase0.indep_states.states:y_58                                                                c     0.000000E+00     1.502346E+05     1.000000E+21           
        139  traj.phases.phase0.indep_states.states:y_59                                                                c     0.000000E+00     1.502346E+05     1.000000E+21           
        140  traj.phases.phase0.indep_states.states:y_60                                                                c     0.000000E+00     1.546235E+05     1.000000E+21           
        141  traj.phases.phase0.indep_states.states:y_61                                                                c     0.000000E+00     1.603061E+05     1.000000E+21           
        142  traj.phases.phase0.indep_states.states:y_62                                                                c     0.000000E+00     1.620065E+05     1.000000E+21           
        143  traj.phases.phase0.indep_states.states:y_63                                                                c     0.000000E+00     1.620065E+05     1.000000E+21           
        144  traj.phases.phase0.indep_states.states:y_64                                                                c     0.000000E+00     1.657096E+05     1.000000E+21           
        145  traj.phases.phase0.indep_states.states:y_65                                                                c     0.000000E+00     1.703556E+05     1.000000E+21           
        146  traj.phases.phase0.indep_states.states:y_66                                                                c     0.000000E+00     1.717075E+05     1.000000E+21           
        147  traj.phases.phase0.indep_states.states:y_67                                                                c     0.000000E+00     1.717075E+05     1.000000E+21           
        148  traj.phases.phase0.indep_states.states:y_68                                                                c     0.000000E+00     1.745788E+05     1.000000E+21           
        149  traj.phases.phase0.indep_states.states:y_69                                                                c     0.000000E+00     1.780058E+05     1.000000E+21           
        150  traj.phases.phase0.indep_states.states:y_70                                                                c     0.000000E+00     1.789562E+05     1.000000E+21           
        151  traj.phases.phase0.indep_states.states:y_71                                                                c     0.000000E+00     1.789562E+05     1.000000E+21           
        152  traj.phases.phase0.indep_states.states:y_72                                                                c     0.000000E+00     1.808822E+05     1.000000E+21           
        153  traj.phases.phase0.indep_states.states:y_73                                                                c     0.000000E+00     1.829511E+05     1.000000E+21           
        154  traj.phases.phase0.indep_states.states:y_74                                                                c     0.000000E+00     1.834600E+05     1.000000E+21           
        155  traj.phases.phase0.indep_states.states:y_75                                                                c     0.000000E+00     1.834600E+05     1.000000E+21           
        156  traj.phases.phase0.indep_states.states:y_76                                                                c     0.000000E+00     1.843555E+05     1.000000E+21           
        157  traj.phases.phase0.indep_states.states:y_77                                                                c     0.000000E+00     1.849625E+05     1.000000E+21           
        158  traj.phases.phase0.indep_states.states:y_78                                                                c     0.000000E+00     1.850000E+05     1.000000E+21           
        159  traj.phases.phase0.indep_states.states:vx_0                                                                c     0.000000E+00     1.433890E+01     1.000000E+21           
        160  traj.phases.phase0.indep_states.states:vx_1                                                                c     0.000000E+00     3.468053E+01     1.000000E+21           
        161  traj.phases.phase0.indep_states.states:vx_2                                                                c     0.000000E+00     4.125858E+01     1.000000E+21           
        162  traj.phases.phase0.indep_states.states:vx_3                                                                c     0.000000E+00     4.125858E+01     1.000000E+21           
        163  traj.phases.phase0.indep_states.states:vx_4                                                                c     0.000000E+00     5.658620E+01     1.000000E+21           
        164  traj.phases.phase0.indep_states.states:vx_5                                                                c     0.000000E+00     7.836602E+01     1.000000E+21           
        165  traj.phases.phase0.indep_states.states:vx_6                                                                c     0.000000E+00     8.541812E+01     1.000000E+21           
        166  traj.phases.phase0.indep_states.states:vx_7                                                                c     0.000000E+00     8.541812E+01     1.000000E+21           
        167  traj.phases.phase0.indep_states.states:vx_8                                                                c     0.000000E+00     1.018675E+02     1.000000E+21           
        168  traj.phases.phase0.indep_states.states:vx_9                                                                c     0.000000E+00     1.252829E+02     1.000000E+21           
        169  traj.phases.phase0.indep_states.states:vx_10                                                               c     0.000000E+00     1.328751E+02     1.000000E+21           
        170  traj.phases.phase0.indep_states.states:vx_11                                                               c     0.000000E+00     1.328751E+02     1.000000E+21           
        171  traj.phases.phase0.indep_states.states:vx_12                                                               c     0.000000E+00     1.506043E+02     1.000000E+21           
        172  traj.phases.phase0.indep_states.states:vx_13                                                               c     0.000000E+00     1.758899E+02     1.000000E+21           
        173  traj.phases.phase0.indep_states.states:vx_14                                                               c     0.000000E+00     1.841006E+02     1.000000E+21           
        174  traj.phases.phase0.indep_states.states:vx_15                                                               c     0.000000E+00     1.841006E+02     1.000000E+21           
        175  traj.phases.phase0.indep_states.states:vx_16                                                               c     0.000000E+00     2.032975E+02     1.000000E+21           
        176  traj.phases.phase0.indep_states.states:vx_17                                                               c     0.000000E+00     2.307320E+02     1.000000E+21           
        177  traj.phases.phase0.indep_states.states:vx_18                                                               c     0.000000E+00     2.396544E+02     1.000000E+21           
        178  traj.phases.phase0.indep_states.states:vx_19                                                               c     0.000000E+00     2.396544E+02     1.000000E+21           
        179  traj.phases.phase0.indep_states.states:vx_20                                                               c     0.000000E+00     2.605416E+02     1.000000E+21           
        180  traj.phases.phase0.indep_states.states:vx_21                                                               c     0.000000E+00     2.904545E+02     1.000000E+21           
        181  traj.phases.phase0.indep_states.states:vx_22                                                               c     0.000000E+00     3.001984E+02     1.000000E+21           
        182  traj.phases.phase0.indep_states.states:vx_23                                                               c     0.000000E+00     3.001984E+02     1.000000E+21           
        183  traj.phases.phase0.indep_states.states:vx_24                                                               c     0.000000E+00     3.230375E+02     1.000000E+21           
        184  traj.phases.phase0.indep_states.states:vx_25                                                               c     0.000000E+00     3.558123E+02     1.000000E+21           
        185  traj.phases.phase0.indep_states.states:vx_26                                                               c     0.000000E+00     3.665047E+02     1.000000E+21           
        186  traj.phases.phase0.indep_states.states:vx_27                                                               c     0.000000E+00     3.665047E+02     1.000000E+21           
        187  traj.phases.phase0.indep_states.states:vx_28                                                               c     0.000000E+00     3.915955E+02     1.000000E+21           
        188  traj.phases.phase0.indep_states.states:vx_29                                                               c     0.000000E+00     4.276649E+02     1.000000E+21           
        189  traj.phases.phase0.indep_states.states:vx_30                                                               c     0.000000E+00     4.394465E+02     1.000000E+21           
        190  traj.phases.phase0.indep_states.states:vx_31                                                               c     0.000000E+00     4.394465E+02     1.000000E+21           
        191  traj.phases.phase0.indep_states.states:vx_32                                                               c     0.000000E+00     4.671160E+02     1.000000E+21           
        192  traj.phases.phase0.indep_states.states:vx_33                                                               c     0.000000E+00     5.069348E+02     1.000000E+21           
        193  traj.phases.phase0.indep_states.states:vx_34                                                               c     0.000000E+00     5.199485E+02     1.000000E+21           
        194  traj.phases.phase0.indep_states.states:vx_35                                                               c     0.000000E+00     5.199485E+02     1.000000E+21           
        195  traj.phases.phase0.indep_states.states:vx_36                                                               c     0.000000E+00     5.505161E+02     1.000000E+21           
        196  traj.phases.phase0.indep_states.states:vx_37                                                               c     0.000000E+00     5.944911E+02     1.000000E+21           
        197  traj.phases.phase0.indep_states.states:vx_38                                                               c     0.000000E+00     6.088531E+02     1.000000E+21           
        198  traj.phases.phase0.indep_states.states:vx_39                                                               c     0.000000E+00     6.088531E+02     1.000000E+21           
        199  traj.phases.phase0.indep_states.states:vx_40                                                               c     0.000000E+00     6.425512E+02     1.000000E+21           
        200  traj.phases.phase0.indep_states.states:vx_41                                                               c     0.000000E+00     6.908955E+02     1.000000E+21           
        201  traj.phases.phase0.indep_states.states:vx_42                                                               c     0.000000E+00     7.066397E+02     1.000000E+21           
        202  traj.phases.phase0.indep_states.states:vx_43                                                               c     0.000000E+00     7.066397E+02     1.000000E+21           
        203  traj.phases.phase0.indep_states.states:vx_44                                                               c     0.000000E+00     7.434669E+02     1.000000E+21           
        204  traj.phases.phase0.indep_states.states:vx_45                                                               c     0.000000E+00     7.959585E+02     1.000000E+21           
        205  traj.phases.phase0.indep_states.states:vx_46                                                               c     0.000000E+00     8.129513E+02     1.000000E+21           
        206  traj.phases.phase0.indep_states.states:vx_47                                                               c     0.000000E+00     8.129513E+02     1.000000E+21           
        207  traj.phases.phase0.indep_states.states:vx_48                                                               c     0.000000E+00     8.524697E+02     1.000000E+21           
        208  traj.phases.phase0.indep_states.states:vx_49                                                               c     0.000000E+00     9.081749E+02     1.000000E+21           
        209  traj.phases.phase0.indep_states.states:vx_50                                                               c     0.000000E+00     9.260352E+02     1.000000E+21           
        210  traj.phases.phase0.indep_states.states:vx_51                                                               c     0.000000E+00     9.260352E+02     1.000000E+21           
        211  traj.phases.phase0.indep_states.states:vx_52                                                               c     0.000000E+00     9.672197E+02     1.000000E+21           
        212  traj.phases.phase0.indep_states.states:vx_53                                                               c     0.000000E+00     1.024402E+03     1.000000E+21           
        213  traj.phases.phase0.indep_states.states:vx_54                                                               c     0.000000E+00     1.042511E+03     1.000000E+21           
        214  traj.phases.phase0.indep_states.states:vx_55                                                               c     0.000000E+00     1.042511E+03     1.000000E+21           
        215  traj.phases.phase0.indep_states.states:vx_56                                                               c     0.000000E+00     1.083856E+03     1.000000E+21           
        216  traj.phases.phase0.indep_states.states:vx_57                                                               c     0.000000E+00     1.140324E+03     1.000000E+21           
        217  traj.phases.phase0.indep_states.states:vx_58                                                               c     0.000000E+00     1.157984E+03     1.000000E+21           
        218  traj.phases.phase0.indep_states.states:vx_59                                                               c     0.000000E+00     1.157984E+03     1.000000E+21           
        219  traj.phases.phase0.indep_states.states:vx_60                                                               c     0.000000E+00     1.197933E+03     1.000000E+21           
        220  traj.phases.phase0.indep_states.states:vx_61                                                               c     0.000000E+00     1.251722E+03     1.000000E+21           
        221  traj.phases.phase0.indep_states.states:vx_62                                                               c     0.000000E+00     1.268376E+03     1.000000E+21           
        222  traj.phases.phase0.indep_states.states:vx_63                                                               c     0.000000E+00     1.268376E+03     1.000000E+21           
        223  traj.phases.phase0.indep_states.states:vx_64                                                               c     0.000000E+00     1.305792E+03     1.000000E+21           
        224  traj.phases.phase0.indep_states.states:vx_65                                                               c     0.000000E+00     1.355673E+03     1.000000E+21           
        225  traj.phases.phase0.indep_states.states:vx_66                                                               c     0.000000E+00     1.371019E+03     1.000000E+21           
        226  traj.phases.phase0.indep_states.states:vx_67                                                               c     0.000000E+00     1.371019E+03     1.000000E+21           
        227  traj.phases.phase0.indep_states.states:vx_68                                                               c     0.000000E+00     1.405356E+03     1.000000E+21           
        228  traj.phases.phase0.indep_states.states:vx_69                                                               c     0.000000E+00     1.450883E+03     1.000000E+21           
        229  traj.phases.phase0.indep_states.states:vx_70                                                               c     0.000000E+00     1.464847E+03     1.000000E+21           
        230  traj.phases.phase0.indep_states.states:vx_71                                                               c     0.000000E+00     1.464847E+03     1.000000E+21           
        231  traj.phases.phase0.indep_states.states:vx_72                                                               c     0.000000E+00     1.496033E+03     1.000000E+21           
        232  traj.phases.phase0.indep_states.states:vx_73                                                               c     0.000000E+00     1.537299E+03     1.000000E+21           
        233  traj.phases.phase0.indep_states.states:vx_74                                                               c     0.000000E+00     1.549945E+03     1.000000E+21           
        234  traj.phases.phase0.indep_states.states:vx_75                                                               c     0.000000E+00     1.549945E+03     1.000000E+21           
        235  traj.phases.phase0.indep_states.states:vx_76                                                               c     0.000000E+00     1.578179E+03     1.000000E+21           
        236  traj.phases.phase0.indep_states.states:vx_77                                                               c     0.000000E+00     1.615544E+03     1.000000E+21           
        237  traj.phases.phase0.indep_states.states:vx_78                                                               c     0.000000E+00     1.627000E+03     1.000000E+21           
        238  traj.phases.phase0.indep_states.states:vy_0                                                                c    -1.000000E+21     2.507046E+01     1.000000E+21           
        239  traj.phases.phase0.indep_states.states:vy_1                                                                c    -1.000000E+21     5.945550E+01     1.000000E+21           
        240  traj.phases.phase0.indep_states.states:vy_2                                                                c    -1.000000E+21     7.028492E+01     1.000000E+21           
        241  traj.phases.phase0.indep_states.states:vy_3                                                                c    -1.000000E+21     7.028492E+01     1.000000E+21           
        242  traj.phases.phase0.indep_states.states:vy_4                                                                c    -1.000000E+21     9.497957E+01     1.000000E+21           
        243  traj.phases.phase0.indep_states.states:vy_5                                                                c    -1.000000E+21     1.287992E+02     1.000000E+21           
        244  traj.phases.phase0.indep_states.states:vy_6                                                                c    -1.000000E+21     1.394373E+02     1.000000E+21           
        245  traj.phases.phase0.indep_states.states:vy_7                                                                c    -1.000000E+21     1.394373E+02     1.000000E+21           
        246  traj.phases.phase0.indep_states.states:vy_8                                                                c    -1.000000E+21     1.636695E+02     1.000000E+21           
        247  traj.phases.phase0.indep_states.states:vy_9                                                                c    -1.000000E+21     1.967898E+02     1.000000E+21           
        248  traj.phases.phase0.indep_states.states:vy_10                                                               c    -1.000000E+21     2.071905E+02     1.000000E+21           
        249  traj.phases.phase0.indep_states.states:vy_11                                                               c    -1.000000E+21     2.071905E+02     1.000000E+21           
        250  traj.phases.phase0.indep_states.states:vy_12                                                               c    -1.000000E+21     2.308468E+02     1.000000E+21           
        251  traj.phases.phase0.indep_states.states:vy_13                                                               c    -1.000000E+21     2.630912E+02     1.000000E+21           
        252  traj.phases.phase0.indep_states.states:vy_14                                                               c    -1.000000E+21     2.731933E+02     1.000000E+21           
        253  traj.phases.phase0.indep_states.states:vy_15                                                               c    -1.000000E+21     2.731933E+02     1.000000E+21           
        254  traj.phases.phase0.indep_states.states:vy_16                                                               c    -1.000000E+21     2.961225E+02     1.000000E+21           
        255  traj.phases.phase0.indep_states.states:vy_17                                                               c    -1.000000E+21     3.272550E+02     1.000000E+21           
        256  traj.phases.phase0.indep_states.states:vy_18                                                               c    -1.000000E+21     3.369762E+02     1.000000E+21           
        257  traj.phases.phase0.indep_states.states:vy_19                                                               c    -1.000000E+21     3.369762E+02     1.000000E+21           
        258  traj.phases.phase0.indep_states.states:vy_20                                                               c    -1.000000E+21     3.589749E+02     1.000000E+21           
        259  traj.phases.phase0.indep_states.states:vy_21                                                               c    -1.000000E+21     3.886752E+02     1.000000E+21           
        260  traj.phases.phase0.indep_states.states:vy_22                                                               c    -1.000000E+21     3.979035E+02     1.000000E+21           
        261  traj.phases.phase0.indep_states.states:vy_23                                                               c    -1.000000E+21     3.979035E+02     1.000000E+21           
        262  traj.phases.phase0.indep_states.states:vy_24                                                               c    -1.000000E+21     4.186936E+02     1.000000E+21           
        263  traj.phases.phase0.indep_states.states:vy_25                                                               c    -1.000000E+21     4.465221E+02     1.000000E+21           
        264  traj.phases.phase0.indep_states.states:vy_26                                                               c    -1.000000E+21     4.551033E+02     1.000000E+21           
        265  traj.phases.phase0.indep_states.states:vy_27                                                               c    -1.000000E+21     4.551033E+02     1.000000E+21           
        266  traj.phases.phase0.indep_states.states:vy_28                                                               c    -1.000000E+21     4.743006E+02     1.000000E+21           
        267  traj.phases.phase0.indep_states.states:vy_29                                                               c    -1.000000E+21     4.996482E+02     1.000000E+21           
        268  traj.phases.phase0.indep_states.states:vy_30                                                               c    -1.000000E+21     5.073683E+02     1.000000E+21           
        269  traj.phases.phase0.indep_states.states:vy_31                                                               c    -1.000000E+21     5.073683E+02     1.000000E+21           
        270  traj.phases.phase0.indep_states.states:vy_32                                                               c    -1.000000E+21     5.244398E+02     1.000000E+21           
        271  traj.phases.phase0.indep_states.states:vy_33                                                               c    -1.000000E+21     5.464619E+02     1.000000E+21           
        272  traj.phases.phase0.indep_states.states:vy_34                                                               c    -1.000000E+21     5.530246E+02     1.000000E+21           
        273  traj.phases.phase0.indep_states.states:vy_35                                                               c    -1.000000E+21     5.530246E+02     1.000000E+21           
        274  traj.phases.phase0.indep_states.states:vy_36                                                               c    -1.000000E+21     5.672345E+02     1.000000E+21           
        275  traj.phases.phase0.indep_states.states:vy_37                                                               c    -1.000000E+21     5.847750E+02     1.000000E+21           
        276  traj.phases.phase0.indep_states.states:vy_38                                                               c    -1.000000E+21     5.897782E+02     1.000000E+21           
        277  traj.phases.phase0.indep_states.states:vy_39                                                               c    -1.000000E+21     5.897782E+02     1.000000E+21           
        278  traj.phases.phase0.indep_states.states:vy_40                                                               c    -1.000000E+21     6.001371E+02     1.000000E+21           
        279  traj.phases.phase0.indep_states.states:vy_41                                                               c    -1.000000E+21     6.116750E+02     1.000000E+21           
        280  traj.phases.phase0.indep_states.states:vy_42                                                               c    -1.000000E+21     6.145997E+02     1.000000E+21           
        281  traj.phases.phase0.indep_states.states:vy_43                                                               c    -1.000000E+21     6.145997E+02     1.000000E+21           
        282  traj.phases.phase0.indep_states.states:vy_44                                                               c    -1.000000E+21     6.198587E+02     1.000000E+21           
        283  traj.phases.phase0.indep_states.states:vy_45                                                               c    -1.000000E+21     6.235577E+02     1.000000E+21           
        284  traj.phases.phase0.indep_states.states:vy_46                                                               c    -1.000000E+21     6.238029E+02     1.000000E+21           
        285  traj.phases.phase0.indep_states.states:vy_47                                                               c    -1.000000E+21     6.238029E+02     1.000000E+21           
        286  traj.phases.phase0.indep_states.states:vy_48                                                               c    -1.000000E+21     6.225753E+02     1.000000E+21           
        287  traj.phases.phase0.indep_states.states:vy_49                                                               c    -1.000000E+21     6.165660E+02     1.000000E+21           
        288  traj.phases.phase0.indep_states.states:vy_50                                                               c    -1.000000E+21     6.135687E+02     1.000000E+21           
        289  traj.phases.phase0.indep_states.states:vy_51                                                               c    -1.000000E+21     6.135687E+02     1.000000E+21           
        290  traj.phases.phase0.indep_states.states:vy_52                                                               c    -1.000000E+21     6.046602E+02     1.000000E+21           
        291  traj.phases.phase0.indep_states.states:vy_53                                                               c    -1.000000E+21     5.876022E+02     1.000000E+21           
        292  traj.phases.phase0.indep_states.states:vy_54                                                               c    -1.000000E+21     5.810350E+02     1.000000E+21           
        293  traj.phases.phase0.indep_states.states:vy_55                                                               c    -1.000000E+21     5.810350E+02     1.000000E+21           
        294  traj.phases.phase0.indep_states.states:vy_56                                                               c    -1.000000E+21     5.639032E+02     1.000000E+21           
        295  traj.phases.phase0.indep_states.states:vy_57                                                               c    -1.000000E+21     5.355666E+02     1.000000E+21           
        296  traj.phases.phase0.indep_states.states:vy_58                                                               c    -1.000000E+21     5.254907E+02     1.000000E+21           
        297  traj.phases.phase0.indep_states.states:vy_59                                                               c    -1.000000E+21     5.254907E+02     1.000000E+21           
        298  traj.phases.phase0.indep_states.states:vy_60                                                               c    -1.000000E+21     5.005069E+02     1.000000E+21           
        299  traj.phases.phase0.indep_states.states:vy_61                                                               c    -1.000000E+21     4.618879E+02     1.000000E+21           
        300  traj.phases.phase0.indep_states.states:vy_62                                                               c    -1.000000E+21     4.487218E+02     1.000000E+21           
        301  traj.phases.phase0.indep_states.states:vy_63                                                               c    -1.000000E+21     4.487218E+02     1.000000E+21           
        302  traj.phases.phase0.indep_states.states:vy_64                                                               c    -1.000000E+21     4.169867E+02     1.000000E+21           
        303  traj.phases.phase0.indep_states.states:vy_65                                                               c    -1.000000E+21     3.698427E+02     1.000000E+21           
        304  traj.phases.phase0.indep_states.states:vy_66                                                               c    -1.000000E+21     3.541771E+02     1.000000E+21           
        305  traj.phases.phase0.indep_states.states:vy_67                                                               c    -1.000000E+21     3.541771E+02     1.000000E+21           
        306  traj.phases.phase0.indep_states.states:vy_68                                                               c    -1.000000E+21     3.170705E+02     1.000000E+21           
        307  traj.phases.phase0.indep_states.states:vy_69                                                               c    -1.000000E+21     2.632979E+02     1.000000E+21           
        308  traj.phases.phase0.indep_states.states:vy_70                                                               c    -1.000000E+21     2.457161E+02     1.000000E+21           
        309  traj.phases.phase0.indep_states.states:vy_71                                                               c    -1.000000E+21     2.457161E+02     1.000000E+21           
        310  traj.phases.phase0.indep_states.states:vy_72                                                               c    -1.000000E+21     2.045276E+02     1.000000E+21           
        311  traj.phases.phase0.indep_states.states:vy_73                                                               c    -1.000000E+21     1.457738E+02     1.000000E+21           
        312  traj.phases.phase0.indep_states.states:vy_74                                                               c    -1.000000E+21     1.267600E+02     1.000000E+21           
        313  traj.phases.phase0.indep_states.states:vy_75                                                               c    -1.000000E+21     1.267600E+02     1.000000E+21           
        314  traj.phases.phase0.indep_states.states:vy_76                                                               c    -1.000000E+21     8.253103E+01     1.000000E+21           
        315  traj.phases.phase0.indep_states.states:vy_77                                                               c    -1.000000E+21     2.007713E+01     1.000000E+21           
        316  traj.phases.phase0.indep_states.states:vy_78                                                               c    -1.000000E+21    -2.646978E-23     1.000000E+21           
        317  traj.phases.phase0.indep_states.states:m_0                                                                 c    -1.000000E+21     4.999872E+04     1.000000E+21           
        318  traj.phases.phase0.indep_states.states:m_1                                                                 c    -1.000000E+21     4.999695E+04     1.000000E+21           
        319  traj.phases.phase0.indep_states.states:m_2                                                                 c    -1.000000E+21     4.999639E+04     1.000000E+21           
        320  traj.phases.phase0.indep_states.states:m_3                                                                 c    -1.000000E+21     4.999639E+04     1.000000E+21           
        321  traj.phases.phase0.indep_states.states:m_4                                                                 c    -1.000000E+21     4.999510E+04     1.000000E+21           
        322  traj.phases.phase0.indep_states.states:m_5                                                                 c    -1.000000E+21     4.999333E+04     1.000000E+21           
        323  traj.phases.phase0.indep_states.states:m_6                                                                 c    -1.000000E+21     4.999277E+04     1.000000E+21           
        324  traj.phases.phase0.indep_states.states:m_7                                                                 c    -1.000000E+21     4.999277E+04     1.000000E+21           
        325  traj.phases.phase0.indep_states.states:m_8                                                                 c    -1.000000E+21     4.999149E+04     1.000000E+21           
        326  traj.phases.phase0.indep_states.states:m_9                                                                 c    -1.000000E+21     4.998972E+04     1.000000E+21           
        327  traj.phases.phase0.indep_states.states:m_10                                                                c    -1.000000E+21     4.998916E+04     1.000000E+21           
        328  traj.phases.phase0.indep_states.states:m_11                                                                c    -1.000000E+21     4.998916E+04     1.000000E+21           
        329  traj.phases.phase0.indep_states.states:m_12                                                                c    -1.000000E+21     4.998788E+04     1.000000E+21           
        330  traj.phases.phase0.indep_states.states:m_13                                                                c    -1.000000E+21     4.998611E+04     1.000000E+21           
        331  traj.phases.phase0.indep_states.states:m_14                                                                c    -1.000000E+21     4.998555E+04     1.000000E+21           
        332  traj.phases.phase0.indep_states.states:m_15                                                                c    -1.000000E+21     4.998555E+04     1.000000E+21           
        333  traj.phases.phase0.indep_states.states:m_16                                                                c    -1.000000E+21     4.998427E+04     1.000000E+21           
        334  traj.phases.phase0.indep_states.states:m_17                                                                c    -1.000000E+21     4.998250E+04     1.000000E+21           
        335  traj.phases.phase0.indep_states.states:m_18                                                                c    -1.000000E+21     4.998194E+04     1.000000E+21           
        336  traj.phases.phase0.indep_states.states:m_19                                                                c    -1.000000E+21     4.998194E+04     1.000000E+21           
        337  traj.phases.phase0.indep_states.states:m_20                                                                c    -1.000000E+21     4.998065E+04     1.000000E+21           
        338  traj.phases.phase0.indep_states.states:m_21                                                                c    -1.000000E+21     4.997888E+04     1.000000E+21           
        339  traj.phases.phase0.indep_states.states:m_22                                                                c    -1.000000E+21     4.997832E+04     1.000000E+21           
        340  traj.phases.phase0.indep_states.states:m_23                                                                c    -1.000000E+21     4.997832E+04     1.000000E+21           
        341  traj.phases.phase0.indep_states.states:m_24                                                                c    -1.000000E+21     4.997704E+04     1.000000E+21           
        342  traj.phases.phase0.indep_states.states:m_25                                                                c    -1.000000E+21     4.997527E+04     1.000000E+21           
        343  traj.phases.phase0.indep_states.states:m_26                                                                c    -1.000000E+21     4.997471E+04     1.000000E+21           
        344  traj.phases.phase0.indep_states.states:m_27                                                                c    -1.000000E+21     4.997471E+04     1.000000E+21           
        345  traj.phases.phase0.indep_states.states:m_28                                                                c    -1.000000E+21     4.997343E+04     1.000000E+21           
        346  traj.phases.phase0.indep_states.states:m_29                                                                c    -1.000000E+21     4.997166E+04     1.000000E+21           
        347  traj.phases.phase0.indep_states.states:m_30                                                                c    -1.000000E+21     4.997110E+04     1.000000E+21           
        348  traj.phases.phase0.indep_states.states:m_31                                                                c    -1.000000E+21     4.997110E+04     1.000000E+21           
        349  traj.phases.phase0.indep_states.states:m_32                                                                c    -1.000000E+21     4.996981E+04     1.000000E+21           
        350  traj.phases.phase0.indep_states.states:m_33                                                                c    -1.000000E+21     4.996804E+04     1.000000E+21           
        351  traj.phases.phase0.indep_states.states:m_34                                                                c    -1.000000E+21     4.996748E+04     1.000000E+21           
        352  traj.phases.phase0.indep_states.states:m_35                                                                c    -1.000000E+21     4.996748E+04     1.000000E+21           
        353  traj.phases.phase0.indep_states.states:m_36                                                                c    -1.000000E+21     4.996620E+04     1.000000E+21           
        354  traj.phases.phase0.indep_states.states:m_37                                                                c    -1.000000E+21     4.996443E+04     1.000000E+21           
        355  traj.phases.phase0.indep_states.states:m_38                                                                c    -1.000000E+21     4.996387E+04     1.000000E+21           
        356  traj.phases.phase0.indep_states.states:m_39                                                                c    -1.000000E+21     4.996387E+04     1.000000E+21           
        357  traj.phases.phase0.indep_states.states:m_40                                                                c    -1.000000E+21     4.996259E+04     1.000000E+21           
        358  traj.phases.phase0.indep_states.states:m_41                                                                c    -1.000000E+21     4.996082E+04     1.000000E+21           
        359  traj.phases.phase0.indep_states.states:m_42                                                                c    -1.000000E+21     4.996026E+04     1.000000E+21           
        360  traj.phases.phase0.indep_states.states:m_43                                                                c    -1.000000E+21     4.996026E+04     1.000000E+21           
        361  traj.phases.phase0.indep_states.states:m_44                                                                c    -1.000000E+21     4.995898E+04     1.000000E+21           
        362  traj.phases.phase0.indep_states.states:m_45                                                                c    -1.000000E+21     4.995721E+04     1.000000E+21           
        363  traj.phases.phase0.indep_states.states:m_46                                                                c    -1.000000E+21     4.995665E+04     1.000000E+21           
        364  traj.phases.phase0.indep_states.states:m_47                                                                c    -1.000000E+21     4.995665E+04     1.000000E+21           
        365  traj.phases.phase0.indep_states.states:m_48                                                                c    -1.000000E+21     4.995536E+04     1.000000E+21           
        366  traj.phases.phase0.indep_states.states:m_49                                                                c    -1.000000E+21     4.995359E+04     1.000000E+21           
        367  traj.phases.phase0.indep_states.states:m_50                                                                c    -1.000000E+21     4.995303E+04     1.000000E+21           
        368  traj.phases.phase0.indep_states.states:m_51                                                                c    -1.000000E+21     4.995303E+04     1.000000E+21           
        369  traj.phases.phase0.indep_states.states:m_52                                                                c    -1.000000E+21     4.995175E+04     1.000000E+21           
        370  traj.phases.phase0.indep_states.states:m_53                                                                c    -1.000000E+21     4.994998E+04     1.000000E+21           
        371  traj.phases.phase0.indep_states.states:m_54                                                                c    -1.000000E+21     4.994942E+04     1.000000E+21           
        372  traj.phases.phase0.indep_states.states:m_55                                                                c    -1.000000E+21     4.994942E+04     1.000000E+21           
        373  traj.phases.phase0.indep_states.states:m_56                                                                c    -1.000000E+21     4.994814E+04     1.000000E+21           
        374  traj.phases.phase0.indep_states.states:m_57                                                                c    -1.000000E+21     4.994637E+04     1.000000E+21           
        375  traj.phases.phase0.indep_states.states:m_58                                                                c    -1.000000E+21     4.994581E+04     1.000000E+21           
        376  traj.phases.phase0.indep_states.states:m_59                                                                c    -1.000000E+21     4.994581E+04     1.000000E+21           
        377  traj.phases.phase0.indep_states.states:m_60                                                                c    -1.000000E+21     4.994452E+04     1.000000E+21           
        378  traj.phases.phase0.indep_states.states:m_61                                                                c    -1.000000E+21     4.994275E+04     1.000000E+21           
        379  traj.phases.phase0.indep_states.states:m_62                                                                c    -1.000000E+21     4.994219E+04     1.000000E+21           
        380  traj.phases.phase0.indep_states.states:m_63                                                                c    -1.000000E+21     4.994219E+04     1.000000E+21           
        381  traj.phases.phase0.indep_states.states:m_64                                                                c    -1.000000E+21     4.994091E+04     1.000000E+21           
        382  traj.phases.phase0.indep_states.states:m_65                                                                c    -1.000000E+21     4.993914E+04     1.000000E+21           
        383  traj.phases.phase0.indep_states.states:m_66                                                                c    -1.000000E+21     4.993858E+04     1.000000E+21           
        384  traj.phases.phase0.indep_states.states:m_67                                                                c    -1.000000E+21     4.993858E+04     1.000000E+21           
        385  traj.phases.phase0.indep_states.states:m_68                                                                c    -1.000000E+21     4.993730E+04     1.000000E+21           
        386  traj.phases.phase0.indep_states.states:m_69                                                                c    -1.000000E+21     4.993553E+04     1.000000E+21           
        387  traj.phases.phase0.indep_states.states:m_70                                                                c    -1.000000E+21     4.993497E+04     1.000000E+21           
        388  traj.phases.phase0.indep_states.states:m_71                                                                c    -1.000000E+21     4.993497E+04     1.000000E+21           
        389  traj.phases.phase0.indep_states.states:m_72                                                                c    -1.000000E+21     4.993369E+04     1.000000E+21           
        390  traj.phases.phase0.indep_states.states:m_73                                                                c    -1.000000E+21     4.993192E+04     1.000000E+21           
        391  traj.phases.phase0.indep_states.states:m_74                                                                c    -1.000000E+21     4.993136E+04     1.000000E+21           
        392  traj.phases.phase0.indep_states.states:m_75                                                                c    -1.000000E+21     4.993136E+04     1.000000E+21           
        393  traj.phases.phase0.indep_states.states:m_76                                                                c    -1.000000E+21     4.993007E+04     1.000000E+21           
        394  traj.phases.phase0.indep_states.states:m_77                                                                c    -1.000000E+21     4.992830E+04     1.000000E+21           
        395  traj.phases.phase0.indep_states.states:m_78                                                                c    -1.000000E+21     4.992774E+04     1.000000E+21           
        396  traj.phases.phase0.polynomial_control_group.indep_polynomial_controls.polynomial_controls:tan_theta_0      c    -1.000000E+21     2.747399E+00     1.000000E+21           
        397  traj.phases.phase0.polynomial_control_group.indep_polynomial_controls.polynomial_controls:tan_theta_1      c    -1.000000E+21    -1.241462E+00     1.000000E+21           

   Constraints (i - inequality, e - equality)
      Index  Name                                                 Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
          0  traj.phases.phase0->final_boundary_constraint->y        e   1.850000E+05    1.850000E+05    1.850000E+05              9.00000E+100
          1  traj.phases.phase0->final_boundary_constraint->vx       e   1.627000E+03    1.627000E+03    1.627000E+03              9.00000E+100
          2  traj.phases.phase0->final_boundary_constraint->vy       e   0.000000E+00   -2.646978E-23    0.000000E+00              9.00000E+100
          3  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          4  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -8.557009E-14    0.000000E+00              9.00000E+100
          5  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -8.557009E-14    0.000000E+00              9.00000E+100
          6  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -1.711402E-13    0.000000E+00              9.00000E+100
          7  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -5.989906E-13    0.000000E+00              9.00000E+100
          8  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    3.422804E-13    0.000000E+00              9.00000E+100
          9  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -8.557009E-13    0.000000E+00              9.00000E+100
         10  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    1.882542E-12    0.000000E+00              9.00000E+100
         11  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    1.026841E-12    0.000000E+00              9.00000E+100
         12  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -9.583850E-12    0.000000E+00              9.00000E+100
         13  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         14  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -3.422804E-13    0.000000E+00              9.00000E+100
         15  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    2.053682E-12    0.000000E+00              9.00000E+100
         16  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    1.369121E-12    0.000000E+00              9.00000E+100
         17  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -6.845607E-13    0.000000E+00              9.00000E+100
         18  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    1.711402E-12    0.000000E+00              9.00000E+100
         19  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -2.053682E-12    0.000000E+00              9.00000E+100
         20  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    5.476486E-12    0.000000E+00              9.00000E+100
         21  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -1.369121E-11    0.000000E+00              9.00000E+100
         22  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    1.369121E-12    0.000000E+00              9.00000E+100
         23  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -1.232209E-11    0.000000E+00              9.00000E+100
         24  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -6.845607E-13    0.000000E+00              9.00000E+100
         25  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    2.738243E-12    0.000000E+00              9.00000E+100
         26  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -6.845607E-13    0.000000E+00              9.00000E+100
         27  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -3.422804E-12    0.000000E+00              9.00000E+100
         28  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -2.738243E-12    0.000000E+00              9.00000E+100
         29  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    4.791925E-12    0.000000E+00              9.00000E+100
         30  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -2.738243E-11    0.000000E+00              9.00000E+100
         31  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         32  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    9.583850E-12    0.000000E+00              9.00000E+100
         33  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    1.779858E-11    0.000000E+00              9.00000E+100
         34  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -1.642946E-11    0.000000E+00              9.00000E+100
         35  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    5.476486E-12    0.000000E+00              9.00000E+100
         36  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    2.053682E-11    0.000000E+00              9.00000E+100
         37  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    1.369121E-12    0.000000E+00              9.00000E+100
         38  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    2.464419E-11    0.000000E+00              9.00000E+100
         39  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         40  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -2.875155E-11    0.000000E+00              9.00000E+100
         41  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    2.601331E-11    0.000000E+00              9.00000E+100
         42  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    6.845607E-12    0.000000E+00              9.00000E+100
         43  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -6.024134E-11    0.000000E+00              9.00000E+100
         44  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    1.095297E-11    0.000000E+00              9.00000E+100
         45  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         46  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    3.285892E-11    0.000000E+00              9.00000E+100
         47  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    1.369121E-11    0.000000E+00              9.00000E+100
         48  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -6.845607E-11    0.000000E+00              9.00000E+100
         49  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    5.202662E-11    0.000000E+00              9.00000E+100
         50  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -8.214729E-12    0.000000E+00              9.00000E+100
         51  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    6.571783E-11    0.000000E+00              9.00000E+100
         52  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -3.012067E-11    0.000000E+00              9.00000E+100
         53  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    1.150062E-10    0.000000E+00              9.00000E+100
         54  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -3.285892E-11    0.000000E+00              9.00000E+100
         55  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -2.190594E-11    0.000000E+00              9.00000E+100
         56  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    7.393256E-11    0.000000E+00              9.00000E+100
         57  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    2.464419E-11    0.000000E+00              9.00000E+100
         58  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    9.036202E-11    0.000000E+00              9.00000E+100
         59  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    2.190594E-11    0.000000E+00              9.00000E+100
         60  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -3.806158E-10    0.000000E+00              9.00000E+100
         61  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00    6.297959E-11    0.000000E+00              9.00000E+100
         62  traj.phases.phase0.collocation_constraint.defects:x     e   0.000000E+00   -1.095297E-10    0.000000E+00              9.00000E+100
         63  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -3.629850E-13    0.000000E+00              9.00000E+100
         64  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         65  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -2.567103E-13    0.000000E+00              9.00000E+100
         66  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    6.845607E-13    0.000000E+00              9.00000E+100
         67  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -5.134206E-13    0.000000E+00              9.00000E+100
         68  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    6.845607E-13    0.000000E+00              9.00000E+100
         69  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -2.053682E-12    0.000000E+00              9.00000E+100
         70  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    1.026841E-12    0.000000E+00              9.00000E+100
         71  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         72  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    2.053682E-12    0.000000E+00              9.00000E+100
         73  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -1.711402E-12    0.000000E+00              9.00000E+100
         74  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -5.476486E-12    0.000000E+00              9.00000E+100
         75  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -2.738243E-12    0.000000E+00              9.00000E+100
         76  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    4.791925E-12    0.000000E+00              9.00000E+100
         77  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -3.422804E-12    0.000000E+00              9.00000E+100
         78  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -1.369121E-11    0.000000E+00              9.00000E+100
         79  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -6.161047E-12    0.000000E+00              9.00000E+100
         80  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -4.791925E-12    0.000000E+00              9.00000E+100
         81  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -2.259050E-11    0.000000E+00              9.00000E+100
         82  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -2.738243E-12    0.000000E+00              9.00000E+100
         83  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -1.985226E-11    0.000000E+00              9.00000E+100
         84  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    4.791925E-12    0.000000E+00              9.00000E+100
         85  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -4.107364E-12    0.000000E+00              9.00000E+100
         86  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -1.300665E-11    0.000000E+00              9.00000E+100
         87  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -2.738243E-12    0.000000E+00              9.00000E+100
         88  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    5.476486E-12    0.000000E+00              9.00000E+100
         89  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -8.214729E-12    0.000000E+00              9.00000E+100
         90  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    2.464419E-11    0.000000E+00              9.00000E+100
         91  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         92  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -5.476486E-12    0.000000E+00              9.00000E+100
         93  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -6.161047E-11    0.000000E+00              9.00000E+100
         94  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    1.232209E-11    0.000000E+00              9.00000E+100
         95  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    8.214729E-12    0.000000E+00              9.00000E+100
         96  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -6.434871E-11    0.000000E+00              9.00000E+100
         97  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    1.916770E-11    0.000000E+00              9.00000E+100
         98  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    6.845607E-12    0.000000E+00              9.00000E+100
         99  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -2.190594E-11    0.000000E+00              9.00000E+100
        100  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    1.779858E-11    0.000000E+00              9.00000E+100
        101  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    1.095297E-11    0.000000E+00              9.00000E+100
        102  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -1.136371E-10    0.000000E+00              9.00000E+100
        103  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    1.369121E-11    0.000000E+00              9.00000E+100
        104  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -2.738243E-12    0.000000E+00              9.00000E+100
        105  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -1.054224E-10    0.000000E+00              9.00000E+100
        106  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -1.506034E-11    0.000000E+00              9.00000E+100
        107  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -4.791925E-11    0.000000E+00              9.00000E+100
        108  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -6.571783E-11    0.000000E+00              9.00000E+100
        109  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -1.506034E-11    0.000000E+00              9.00000E+100
        110  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    8.146273E-11    0.000000E+00              9.00000E+100
        111  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -1.642946E-10    0.000000E+00              9.00000E+100
        112  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -5.681854E-11    0.000000E+00              9.00000E+100
        113  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    5.134206E-11    0.000000E+00              9.00000E+100
        114  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -5.271118E-11    0.000000E+00              9.00000E+100
        115  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -3.285892E-11    0.000000E+00              9.00000E+100
        116  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    2.122138E-11    0.000000E+00              9.00000E+100
        117  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -8.625465E-11    0.000000E+00              9.00000E+100
        118  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    2.875155E-11    0.000000E+00              9.00000E+100
        119  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    5.818766E-12    0.000000E+00              9.00000E+100
        120  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00   -1.134659E-10    0.000000E+00              9.00000E+100
        121  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    2.053682E-11    0.000000E+00              9.00000E+100
        122  traj.phases.phase0.collocation_constraint.defects:y     e   0.000000E+00    1.792693E-11    0.000000E+00              9.00000E+100
        123  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -1.069626E-14    0.000000E+00              9.00000E+100
        124  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    2.139252E-14    0.000000E+00              9.00000E+100
        125  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -5.348131E-15    0.000000E+00              9.00000E+100
        126  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    5.348131E-14    0.000000E+00              9.00000E+100
        127  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    2.139252E-14    0.000000E+00              9.00000E+100
        128  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    3.743692E-14    0.000000E+00              9.00000E+100
        129  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -3.476285E-14    0.000000E+00              9.00000E+100
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        147  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -1.604439E-13    0.000000E+00              9.00000E+100
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        150  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    4.385467E-13    0.000000E+00              9.00000E+100
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        152  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    2.085771E-13    0.000000E+00              9.00000E+100
        153  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    1.069626E-14    0.000000E+00              9.00000E+100
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        158  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -4.492430E-13    0.000000E+00              9.00000E+100
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        160  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    2.139252E-13    0.000000E+00              9.00000E+100
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        162  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    1.283551E-13    0.000000E+00              9.00000E+100
        163  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -1.604439E-13    0.000000E+00              9.00000E+100
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        165  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    4.385467E-13    0.000000E+00              9.00000E+100
        166  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -1.283551E-13    0.000000E+00              9.00000E+100
        167  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -2.887991E-13    0.000000E+00              9.00000E+100
        168  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    4.385467E-13    0.000000E+00              9.00000E+100
        169  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -3.636729E-13    0.000000E+00              9.00000E+100
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        171  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    1.283551E-12    0.000000E+00              9.00000E+100
        172  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -2.674065E-13    0.000000E+00              9.00000E+100
        173  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    3.422804E-13    0.000000E+00              9.00000E+100
        174  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -3.636729E-13    0.000000E+00              9.00000E+100
        175  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    4.331986E-13    0.000000E+00              9.00000E+100
        176  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    3.422804E-13    0.000000E+00              9.00000E+100
        177  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    1.497477E-13    0.000000E+00              9.00000E+100
        178  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -1.604439E-14    0.000000E+00              9.00000E+100
        179  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -8.022196E-14    0.000000E+00              9.00000E+100
        180  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    3.048435E-13    0.000000E+00              9.00000E+100
        181  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00    1.069626E-13    0.000000E+00              9.00000E+100
        182  traj.phases.phase0.collocation_constraint.defects:vx    e   0.000000E+00   -7.487383E-14    0.000000E+00              9.00000E+100
        183  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        184  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    1.604439E-14    0.000000E+00              9.00000E+100
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        187  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    2.139252E-14    0.000000E+00              9.00000E+100
        188  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -4.278505E-14    0.000000E+00              9.00000E+100
        189  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    1.283551E-13    0.000000E+00              9.00000E+100
        190  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -2.674065E-14    0.000000E+00              9.00000E+100
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        192  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    4.813318E-14    0.000000E+00              9.00000E+100
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        196  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -1.069626E-13    0.000000E+00              9.00000E+100
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        198  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    1.550958E-13    0.000000E+00              9.00000E+100
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        204  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    6.952570E-14    0.000000E+00              9.00000E+100
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        211  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    1.096367E-13    0.000000E+00              9.00000E+100
        212  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -4.545911E-14    0.000000E+00              9.00000E+100
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        214  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    8.022196E-14    0.000000E+00              9.00000E+100
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        217  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    2.186048E-13    0.000000E+00              9.00000E+100
        218  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -1.253468E-13    0.000000E+00              9.00000E+100
        219  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -4.638877E-13    0.000000E+00              9.00000E+100
        220  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    9.894042E-14    0.000000E+00              9.00000E+100
        221  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -1.524217E-13    0.000000E+00              9.00000E+100
        222  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    1.123107E-13    0.000000E+00              9.00000E+100
        223  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -2.674065E-14    0.000000E+00              9.00000E+100
        224  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    2.647325E-13    0.000000E+00              9.00000E+100
        225  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    1.310292E-13    0.000000E+00              9.00000E+100
        226  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -5.882944E-14    0.000000E+00              9.00000E+100
        227  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    3.743692E-14    0.000000E+00              9.00000E+100
        228  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -8.022196E-14    0.000000E+00              9.00000E+100
        229  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    1.069626E-14    0.000000E+00              9.00000E+100
        230  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -1.337033E-13    0.000000E+00              9.00000E+100
        231  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    2.674065E-14    0.000000E+00              9.00000E+100
        232  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -2.139252E-14    0.000000E+00              9.00000E+100
        233  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    8.557009E-14    0.000000E+00              9.00000E+100
        234  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    1.283551E-13    0.000000E+00              9.00000E+100
        235  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -2.139252E-14    0.000000E+00              9.00000E+100
        236  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    4.278505E-14    0.000000E+00              9.00000E+100
        237  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    1.069626E-13    0.000000E+00              9.00000E+100
        238  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        239  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00   -2.139252E-14    0.000000E+00              9.00000E+100
        240  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    4.278505E-14    0.000000E+00              9.00000E+100
        241  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        242  traj.phases.phase0.collocation_constraint.defects:vy    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        243  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    2.358994E-11    0.000000E+00              9.00000E+100
        244  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    1.762209E-12    0.000000E+00              9.00000E+100
        245  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.038007E-12    0.000000E+00              9.00000E+100
        246  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.513923E-12    0.000000E+00              9.00000E+100
        247  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    1.762209E-12    0.000000E+00              9.00000E+100
        248  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.513923E-12    0.000000E+00              9.00000E+100
        249  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    5.269580E-11    0.000000E+00              9.00000E+100
        250  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.511583E-12    0.000000E+00              9.00000E+100
        251  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.040012E-12    0.000000E+00              9.00000E+100
        252  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    3.814187E-11    0.000000E+00              9.00000E+100
        253  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -2.006585E-11    0.000000E+00              9.00000E+100
        254  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.038007E-12    0.000000E+00              9.00000E+100
        255  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -2.006585E-11    0.000000E+00              9.00000E+100
        256  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.038007E-12    0.000000E+00              9.00000E+100
        257  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.513923E-12    0.000000E+00              9.00000E+100
        258  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.511583E-12    0.000000E+00              9.00000E+100
        259  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.511583E-12    0.000000E+00              9.00000E+100
        260  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.511583E-12    0.000000E+00              9.00000E+100
        261  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    6.724572E-11    0.000000E+00              9.00000E+100
        262  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.513923E-12    0.000000E+00              9.00000E+100
        263  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    2.358994E-11    0.000000E+00              9.00000E+100
        264  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.038007E-12    0.000000E+00              9.00000E+100
        265  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.513923E-12    0.000000E+00              9.00000E+100
        266  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -2.006585E-11    0.000000E+00              9.00000E+100
        267  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.513923E-12    0.000000E+00              9.00000E+100
        268  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -1.278972E-11    0.000000E+00              9.00000E+100
        269  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.038007E-12    0.000000E+00              9.00000E+100
        270  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.513923E-12    0.000000E+00              9.00000E+100
        271  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    1.762209E-12    0.000000E+00              9.00000E+100
        272  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -2.006585E-11    0.000000E+00              9.00000E+100
        273  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.511583E-12    0.000000E+00              9.00000E+100
        274  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    1.764215E-12    0.000000E+00              9.00000E+100
        275  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.040012E-12    0.000000E+00              9.00000E+100
        276  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -4.916737E-11    0.000000E+00              9.00000E+100
        277  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.511583E-12    0.000000E+00              9.00000E+100
        278  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.040012E-12    0.000000E+00              9.00000E+100
        279  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.036335E-12    0.000000E+00              9.00000E+100
        280  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.036335E-12    0.000000E+00              9.00000E+100
        281  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.515594E-12    0.000000E+00              9.00000E+100
        282  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -3.461544E-11    0.000000E+00              9.00000E+100
        283  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    1.631614E-11    0.000000E+00              9.00000E+100
        284  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.511583E-12    0.000000E+00              9.00000E+100
        285  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -2.006752E-11    0.000000E+00              9.00000E+100
        286  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    1.760204E-12    0.000000E+00              9.00000E+100
        287  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.036335E-12    0.000000E+00              9.00000E+100
        288  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -4.916737E-11    0.000000E+00              9.00000E+100
        289  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    1.764215E-12    0.000000E+00              9.00000E+100
        290  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.511583E-12    0.000000E+00              9.00000E+100
        291  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.511583E-12    0.000000E+00              9.00000E+100
        292  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    1.764215E-12    0.000000E+00              9.00000E+100
        293  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    2.359194E-11    0.000000E+00              9.00000E+100
        294  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.036335E-12    0.000000E+00              9.00000E+100
        295  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.515594E-12    0.000000E+00              9.00000E+100
        296  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.515594E-12    0.000000E+00              9.00000E+100
        297  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.040012E-12    0.000000E+00              9.00000E+100
        298  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -1.278771E-11    0.000000E+00              9.00000E+100
        299  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    9.040012E-12    0.000000E+00              9.00000E+100
        300  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00    2.358793E-11    0.000000E+00              9.00000E+100
        301  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.515594E-12    0.000000E+00              9.00000E+100
        302  traj.phases.phase0.collocation_constraint.defects:m     e   0.000000E+00   -5.515594E-12    0.000000E+00              9.00000E+100
        303  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        304  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        305  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        306  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        307  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        308  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        309  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        310  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        311  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        312  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        313  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        314  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        315  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        316  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        317  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        318  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        319  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        320  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        321  traj.phases.phase0.continuity_comp.defect_states:x      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        322  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        323  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        324  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        325  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        326  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        327  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        328  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        329  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        330  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        331  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        332  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        333  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        334  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        335  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        336  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        337  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        338  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        339  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        340  traj.phases.phase0.continuity_comp.defect_states:y      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        341  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        342  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        343  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        344  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        345  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        346  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        347  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        348  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        349  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        350  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        351  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        352  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        353  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        354  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        355  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        356  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        357  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        358  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        359  traj.phases.phase0.continuity_comp.defect_states:vx     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        360  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        361  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        362  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        363  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        364  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        365  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        366  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        367  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        368  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        369  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        370  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        371  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        372  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        373  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        374  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        375  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        376  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        377  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        378  traj.phases.phase0.continuity_comp.defect_states:vy     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        379  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        380  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        381  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        382  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        383  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        384  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        385  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        386  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        387  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        388  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        389  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        390  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        391  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        392  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        393  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        394  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        395  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        396  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        397  traj.phases.phase0.continuity_comp.defect_states:m      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100


   Exit Status
      Inform  Description
           0  Optimization terminated successfully.
--------------------------------------------------------------------------------
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/visualization/opt_report/opt_report.py:634: UserWarning: Attempting to set identical low and high ylims makes transformation singular; automatically expanding.
  ax.set_ylim([ymin_plot, ymax_plot])
Simulating trajectory traj
Done simulating trajectory traj
False
sol = om.CaseReader('dymos_solution.db').get_case('final')
sim = om.CaseReader('dymos_simulation.db').get_case('final')

fig, [traj_ax, control_ax, param_ax] = plt.subplots(nrows=3, ncols=1, figsize=(10, 8))

traj_ax.plot(sol.get_val('traj.phase0.timeseries.states:x'),
             sol.get_val('traj.phase0.timeseries.states:y'),
             marker='o',
             ms=4,
             linestyle='None',
             label='solution')

traj_ax.plot(sim.get_val('traj.phase0.timeseries.states:x'),
             sim.get_val('traj.phase0.timeseries.states:y'),
             marker=None,
             linestyle='-',
             label='simulation')

traj_ax.set_xlabel('range (m)')
traj_ax.set_ylabel('altitude (m)')
traj_ax.set_aspect('equal')
traj_ax.grid(True)

control_ax.plot(sol.get_val('traj.phase0.timeseries.time'),
             sol.get_val('traj.phase0.timeseries.theta'),
             marker='o',
             ms=4,
             linestyle='None')

control_ax.plot(sim.get_val('traj.phase0.timeseries.time'),
             sim.get_val('traj.phase0.timeseries.theta'),
             linestyle='-',
             marker=None)

control_ax.set_ylabel(r'$\theta$ (deg)')
control_ax.grid(True)

tan_theta_sol = sol.get_val('traj.phase0.timeseries.polynomial_controls:tan_theta')
tan_theta_sim = sim.get_val('traj.phase0.timeseries.polynomial_controls:tan_theta')

param_ax.plot(sol.get_val('traj.phase0.timeseries.time'),
             tan_theta_sol,
             marker='o',
             ms=4,
             linestyle='None')

param_ax.plot(sim.get_val('traj.phase0.timeseries.time'),
             tan_theta_sim,
             linestyle='-',
             marker=None)

param_ax.set_xlabel('time (s)')
param_ax.set_ylabel(r'$tan(\theta)$')
param_ax.grid(True)

plt.suptitle('Single Stage to Orbit Solution Using a Polynomial Control')
fig.legend(loc='lower center', ncol=2)

plt.show()
../../_images/1becdfb3505a9018547df0ec55bea22a061f7f80b1519c17b4b2944eed7485a6.png