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

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

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

val=np.zeros(nn),
desc='pitch angle',

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

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

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

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

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

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

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']

theta={'val': np.ones(nn),
tan_theta={'val': np.ones(nn)}))

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

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

phase = dm.Phase(ode_class=LaunchVehicleLinearTangentODE,

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.
#
units='m/s', targets=['eom.vx'])
units='m/s', targets=['eom.vy'])
units='kg', targets=['eom.m'])

#
# The tangent of theta is modeled as a linear polynomial over the duration of the phase.
#
targets=['guidance.tan_theta'], control_type='polynomial')

#
# 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'])

#
# 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.
#

#
# Add theta as a timeseries output since it's not included by default.
#

#
# 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)

#
#
phase.set_time_val(initial=0.0, duration=500.0)
phase.set_state_val('x', [0, 350000.0])
phase.set_state_val('y', [0, 185000.0])
phase.set_state_val('vx', [0, 1627.0])
phase.set_state_val('vy', [1.0E-6, 0.0])
phase.set_state_val('m', 50000)
phase.set_control_val('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: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
INFO: checking unserializable_options
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
Model viewer data has already been recorded for Driver.
INFO: checking out_of_order
INFO: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
INFO: checking unserializable_options
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
Full total jacobian for problem 'problem' was computed 3 times, taking 0.13202635999994072 seconds.
Total jacobian shape: (303, 398)
Jacobian shape: (303, 398)  (1.63% nonzero)
FWD solves: 10   REV solves: 0
Total colors vs. total size: 10 vs 398  (97.49% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity:   0.1320 sec
Time to compute coloring:   0.2699 sec
Memory to compute coloring:   0.8750 MB
Coloring created on: 2024-07-10 17:17:39
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc

Solution:
--------------------------------------------------------------------------------
Total Time:                    1.0014
User Objective Time :       0.0100
User Sensitivity Time :     0.0394
Interface Time :            0.0334
Opt Solver Time:            0.9186
Calls to Objective Function :       6
Calls to Sens Function :            5

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

Variables (c - continuous, i - integer, d - discrete)
Index  Name                               Type      Lower Bound            Value      Upper Bound     Status
0  traj.phase0.t_duration_0              c     1.000000E+01     4.817168E+02     1.000000E+03
1  traj.phase0.states:x_0                c     0.000000E+00     6.106930E+01     1.000000E+21
2  traj.phase0.states:x_1                c     0.000000E+00     3.496393E+02     1.000000E+21
3  traj.phase0.states:x_2                c     0.000000E+00     4.914075E+02     1.000000E+21
4  traj.phase0.states:x_3                c     0.000000E+00     4.914075E+02     1.000000E+21
5  traj.phase0.states:x_4                c     0.000000E+00     9.095034E+02     1.000000E+21
6  traj.phase0.states:x_5                c     0.000000E+00     1.704975E+03     1.000000E+21
7  traj.phase0.states:x_6                c     0.000000E+00     2.010769E+03     1.000000E+21
8  traj.phase0.states:x_7                c     0.000000E+00     2.010769E+03     1.000000E+21
9  traj.phase0.states:x_8                c     0.000000E+00     2.811263E+03     1.000000E+21
10  traj.phase0.states:x_9                c     0.000000E+00     4.150586E+03     1.000000E+21
11  traj.phase0.states:x_10               c     0.000000E+00     4.632596E+03     1.000000E+21
12  traj.phase0.states:x_11               c     0.000000E+00     4.632596E+03     1.000000E+21
13  traj.phase0.states:x_12               c     0.000000E+00     5.844355E+03     1.000000E+21
14  traj.phase0.states:x_13               c     0.000000E+00     7.769668E+03     1.000000E+21
15  traj.phase0.states:x_14               c     0.000000E+00     8.441819E+03     1.000000E+21
16  traj.phase0.states:x_15               c     0.000000E+00     8.441819E+03     1.000000E+21
17  traj.phase0.states:x_16               c     0.000000E+00     1.009787E+04     1.000000E+21
18  traj.phase0.states:x_17               c     0.000000E+00     1.265747E+04     1.000000E+21
19  traj.phase0.states:x_18               c     0.000000E+00     1.353576E+04     1.000000E+21
20  traj.phase0.states:x_19               c     0.000000E+00     1.353576E+04     1.000000E+21
21  traj.phase0.states:x_20               c     0.000000E+00     1.567405E+04     1.000000E+21
22  traj.phase0.states:x_21               c     0.000000E+00     1.892357E+04     1.000000E+21
23  traj.phase0.states:x_22               c     0.000000E+00     2.002641E+04     1.000000E+21
24  traj.phase0.states:x_23               c     0.000000E+00     2.002641E+04     1.000000E+21
25  traj.phase0.states:x_24               c     0.000000E+00     2.269073E+04     1.000000E+21
26  traj.phase0.states:x_25               c     0.000000E+00     2.669437E+04     1.000000E+21
27  traj.phase0.states:x_26               c     0.000000E+00     2.804305E+04     1.000000E+21
28  traj.phase0.states:x_27               c     0.000000E+00     2.804305E+04     1.000000E+21
29  traj.phase0.states:x_28               c     0.000000E+00     3.128395E+04     1.000000E+21
30  traj.phase0.states:x_29               c     0.000000E+00     3.611577E+04     1.000000E+21
31  traj.phase0.states:x_30               c     0.000000E+00     3.773482E+04     1.000000E+21
32  traj.phase0.states:x_31               c     0.000000E+00     3.773482E+04     1.000000E+21
33  traj.phase0.states:x_32               c     0.000000E+00     4.161043E+04     1.000000E+21
34  traj.phase0.states:x_33               c     0.000000E+00     4.735527E+04     1.000000E+21
35  traj.phase0.states:x_34               c     0.000000E+00     4.927265E+04     1.000000E+21
36  traj.phase0.states:x_35               c     0.000000E+00     4.927265E+04     1.000000E+21
37  traj.phase0.states:x_36               c     0.000000E+00     5.384901E+04     1.000000E+21
38  traj.phase0.states:x_37               c     0.000000E+00     6.060228E+04     1.000000E+21
39  traj.phase0.states:x_38               c     0.000000E+00     6.284916E+04     1.000000E+21
40  traj.phase0.states:x_39               c     0.000000E+00     6.284916E+04     1.000000E+21
41  traj.phase0.states:x_40               c     0.000000E+00     6.819918E+04     1.000000E+21
42  traj.phase0.states:x_41               c     0.000000E+00     7.606414E+04     1.000000E+21
43  traj.phase0.states:x_42               c     0.000000E+00     7.867365E+04     1.000000E+21
44  traj.phase0.states:x_43               c     0.000000E+00     7.867365E+04     1.000000E+21
45  traj.phase0.states:x_44               c     0.000000E+00     8.487336E+04     1.000000E+21
46  traj.phase0.states:x_45               c     0.000000E+00     9.395375E+04     1.000000E+21
47  traj.phase0.states:x_46               c     0.000000E+00     9.695801E+04     1.000000E+21
48  traj.phase0.states:x_47               c     0.000000E+00     9.695801E+04     1.000000E+21
49  traj.phase0.states:x_48               c     0.000000E+00     1.040786E+05     1.000000E+21
50  traj.phase0.states:x_49               c     0.000000E+00     1.144647E+05     1.000000E+21
51  traj.phase0.states:x_50               c     0.000000E+00     1.178897E+05     1.000000E+21
52  traj.phase0.states:x_51               c     0.000000E+00     1.178897E+05     1.000000E+21
53  traj.phase0.states:x_52               c     0.000000E+00     1.259848E+05     1.000000E+21
54  traj.phase0.states:x_53               c     0.000000E+00     1.377346E+05     1.000000E+21
55  traj.phase0.states:x_54               c     0.000000E+00     1.415942E+05     1.000000E+21
56  traj.phase0.states:x_55               c     0.000000E+00     1.415942E+05     1.000000E+21
57  traj.phase0.states:x_56               c     0.000000E+00     1.506865E+05     1.000000E+21
58  traj.phase0.states:x_57               c     0.000000E+00     1.638094E+05     1.000000E+21
59  traj.phase0.states:x_58               c     0.000000E+00     1.681011E+05     1.000000E+21
60  traj.phase0.states:x_59               c     0.000000E+00     1.681011E+05     1.000000E+21
61  traj.phase0.states:x_60               c     0.000000E+00     1.781752E+05     1.000000E+21
62  traj.phase0.states:x_61               c     0.000000E+00     1.926292E+05     1.000000E+21
63  traj.phase0.states:x_62               c     0.000000E+00     1.973350E+05     1.000000E+21
64  traj.phase0.states:x_63               c     0.000000E+00     1.973350E+05     1.000000E+21
65  traj.phase0.states:x_64               c     0.000000E+00     2.083426E+05     1.000000E+21
66  traj.phase0.states:x_65               c     0.000000E+00     2.240467E+05     1.000000E+21
67  traj.phase0.states:x_66               c     0.000000E+00     2.291382E+05     1.000000E+21
68  traj.phase0.states:x_67               c     0.000000E+00     2.291382E+05     1.000000E+21
69  traj.phase0.states:x_68               c     0.000000E+00     2.410104E+05     1.000000E+21
70  traj.phase0.states:x_69               c     0.000000E+00     2.578637E+05     1.000000E+21
71  traj.phase0.states:x_70               c     0.000000E+00     2.633083E+05     1.000000E+21
72  traj.phase0.states:x_71               c     0.000000E+00     2.633083E+05     1.000000E+21
73  traj.phase0.states:x_72               c     0.000000E+00     2.759693E+05     1.000000E+21
74  traj.phase0.states:x_73               c     0.000000E+00     2.938674E+05     1.000000E+21
75  traj.phase0.states:x_74               c     0.000000E+00     2.996321E+05     1.000000E+21
76  traj.phase0.states:x_75               c     0.000000E+00     2.996321E+05     1.000000E+21
77  traj.phase0.states:x_76               c     0.000000E+00     3.130082E+05     1.000000E+21
78  traj.phase0.states:x_77               c     0.000000E+00     3.318524E+05     1.000000E+21
79  traj.phase0.states:x_78               c     0.000000E+00     3.379071E+05     1.000000E+21
80  traj.phase0.states:y_0                c     0.000000E+00     1.072874E+02     1.000000E+21
81  traj.phase0.states:y_1                c     0.000000E+00     6.062100E+02     1.000000E+21
82  traj.phase0.states:y_2                c     0.000000E+00     8.484836E+02     1.000000E+21
83  traj.phase0.states:y_3                c     0.000000E+00     8.484836E+02     1.000000E+21
84  traj.phase0.states:y_4                c     0.000000E+00     1.555240E+03     1.000000E+21
85  traj.phase0.states:y_5                c     0.000000E+00     2.875780E+03     1.000000E+21
86  traj.phase0.states:y_6                c     0.000000E+00     3.376666E+03     1.000000E+21
87  traj.phase0.states:y_7                c     0.000000E+00     3.376666E+03     1.000000E+21
88  traj.phase0.states:y_8                c     0.000000E+00     4.672843E+03     1.000000E+21
89  traj.phase0.states:y_9                c     0.000000E+00     6.799841E+03     1.000000E+21
90  traj.phase0.states:y_10               c     0.000000E+00     7.554202E+03     1.000000E+21
91  traj.phase0.states:y_11               c     0.000000E+00     7.554202E+03     1.000000E+21
92  traj.phase0.states:y_12               c     0.000000E+00     9.427357E+03     1.000000E+21
93  traj.phase0.states:y_13               c     0.000000E+00     1.234194E+04     1.000000E+21
94  traj.phase0.states:y_14               c     0.000000E+00     1.334336E+04     1.000000E+21
95  traj.phase0.states:y_15               c     0.000000E+00     1.334336E+04     1.000000E+21
96  traj.phase0.states:y_16               c     0.000000E+00     1.577789E+04     1.000000E+21
97  traj.phase0.states:y_17               c     0.000000E+00     1.945627E+04     1.000000E+21
98  traj.phase0.states:y_18               c     0.000000E+00     2.069660E+04     1.000000E+21
99  traj.phase0.states:y_19               c     0.000000E+00     2.069660E+04     1.000000E+21
100  traj.phase0.states:y_20               c     0.000000E+00     2.367267E+04     1.000000E+21
101  traj.phase0.states:y_21               c     0.000000E+00     2.808440E+04     1.000000E+21
102  traj.phase0.states:y_22               c     0.000000E+00     2.955320E+04     1.000000E+21
103  traj.phase0.states:y_23               c     0.000000E+00     2.955320E+04     1.000000E+21
104  traj.phase0.states:y_24               c     0.000000E+00     3.304522E+04     1.000000E+21
105  traj.phase0.states:y_25               c     0.000000E+00     3.815080E+04     1.000000E+21
106  traj.phase0.states:y_26               c     0.000000E+00     3.983445E+04     1.000000E+21
107  traj.phase0.states:y_27               c     0.000000E+00     3.983445E+04     1.000000E+21
108  traj.phase0.states:y_28               c     0.000000E+00     4.380893E+04     1.000000E+21
109  traj.phase0.states:y_29               c     0.000000E+00     4.955634E+04     1.000000E+21
110  traj.phase0.states:y_30               c     0.000000E+00     5.143680E+04     1.000000E+21
111  traj.phase0.states:y_31               c     0.000000E+00     5.143680E+04     1.000000E+21
112  traj.phase0.states:y_32               c     0.000000E+00     5.584932E+04     1.000000E+21
113  traj.phase0.states:y_33               c     0.000000E+00     6.216918E+04     1.000000E+21
114  traj.phase0.states:y_34               c     0.000000E+00     6.422234E+04     1.000000E+21
115  traj.phase0.states:y_35               c     0.000000E+00     6.422234E+04     1.000000E+21
116  traj.phase0.states:y_36               c     0.000000E+00     6.901329E+04     1.000000E+21
117  traj.phase0.states:y_37               c     0.000000E+00     7.581228E+04     1.000000E+21
118  traj.phase0.states:y_38               c     0.000000E+00     7.800565E+04     1.000000E+21
119  traj.phase0.states:y_39               c     0.000000E+00     7.800565E+04     1.000000E+21
120  traj.phase0.states:y_40               c     0.000000E+00     8.309475E+04     1.000000E+21
121  traj.phase0.states:y_41               c     0.000000E+00     9.024734E+04     1.000000E+21
122  traj.phase0.states:y_42               c     0.000000E+00     9.253734E+04     1.000000E+21
123  traj.phase0.states:y_43               c     0.000000E+00     9.253734E+04     1.000000E+21
124  traj.phase0.states:y_44               c     0.000000E+00     9.781724E+04     1.000000E+21
125  traj.phase0.states:y_45               c     0.000000E+00     1.051572E+05     1.000000E+21
126  traj.phase0.states:y_46               c     0.000000E+00     1.074866E+05     1.000000E+21
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327  traj.phase0.states:m_10               c    -1.000000E+21     4.998916E+04     1.000000E+21
328  traj.phase0.states:m_11               c    -1.000000E+21     4.998916E+04     1.000000E+21
329  traj.phase0.states:m_12               c    -1.000000E+21     4.998788E+04     1.000000E+21
330  traj.phase0.states:m_13               c    -1.000000E+21     4.998611E+04     1.000000E+21
331  traj.phase0.states:m_14               c    -1.000000E+21     4.998555E+04     1.000000E+21
332  traj.phase0.states:m_15               c    -1.000000E+21     4.998555E+04     1.000000E+21
333  traj.phase0.states:m_16               c    -1.000000E+21     4.998427E+04     1.000000E+21
334  traj.phase0.states:m_17               c    -1.000000E+21     4.998250E+04     1.000000E+21
335  traj.phase0.states:m_18               c    -1.000000E+21     4.998194E+04     1.000000E+21
336  traj.phase0.states:m_19               c    -1.000000E+21     4.998194E+04     1.000000E+21
337  traj.phase0.states:m_20               c    -1.000000E+21     4.998065E+04     1.000000E+21
338  traj.phase0.states:m_21               c    -1.000000E+21     4.997888E+04     1.000000E+21
339  traj.phase0.states:m_22               c    -1.000000E+21     4.997832E+04     1.000000E+21
340  traj.phase0.states:m_23               c    -1.000000E+21     4.997832E+04     1.000000E+21
341  traj.phase0.states:m_24               c    -1.000000E+21     4.997704E+04     1.000000E+21
342  traj.phase0.states:m_25               c    -1.000000E+21     4.997527E+04     1.000000E+21
343  traj.phase0.states:m_26               c    -1.000000E+21     4.997471E+04     1.000000E+21
344  traj.phase0.states:m_27               c    -1.000000E+21     4.997471E+04     1.000000E+21
345  traj.phase0.states:m_28               c    -1.000000E+21     4.997343E+04     1.000000E+21
346  traj.phase0.states:m_29               c    -1.000000E+21     4.997166E+04     1.000000E+21
347  traj.phase0.states:m_30               c    -1.000000E+21     4.997110E+04     1.000000E+21
348  traj.phase0.states:m_31               c    -1.000000E+21     4.997110E+04     1.000000E+21
349  traj.phase0.states:m_32               c    -1.000000E+21     4.996981E+04     1.000000E+21
350  traj.phase0.states:m_33               c    -1.000000E+21     4.996804E+04     1.000000E+21
351  traj.phase0.states:m_34               c    -1.000000E+21     4.996748E+04     1.000000E+21
352  traj.phase0.states:m_35               c    -1.000000E+21     4.996748E+04     1.000000E+21
353  traj.phase0.states:m_36               c    -1.000000E+21     4.996620E+04     1.000000E+21
354  traj.phase0.states:m_37               c    -1.000000E+21     4.996443E+04     1.000000E+21
355  traj.phase0.states:m_38               c    -1.000000E+21     4.996387E+04     1.000000E+21
356  traj.phase0.states:m_39               c    -1.000000E+21     4.996387E+04     1.000000E+21
357  traj.phase0.states:m_40               c    -1.000000E+21     4.996259E+04     1.000000E+21
358  traj.phase0.states:m_41               c    -1.000000E+21     4.996082E+04     1.000000E+21
359  traj.phase0.states:m_42               c    -1.000000E+21     4.996026E+04     1.000000E+21
360  traj.phase0.states:m_43               c    -1.000000E+21     4.996026E+04     1.000000E+21
361  traj.phase0.states:m_44               c    -1.000000E+21     4.995898E+04     1.000000E+21
362  traj.phase0.states:m_45               c    -1.000000E+21     4.995721E+04     1.000000E+21
363  traj.phase0.states:m_46               c    -1.000000E+21     4.995665E+04     1.000000E+21
364  traj.phase0.states:m_47               c    -1.000000E+21     4.995665E+04     1.000000E+21
365  traj.phase0.states:m_48               c    -1.000000E+21     4.995536E+04     1.000000E+21
366  traj.phase0.states:m_49               c    -1.000000E+21     4.995359E+04     1.000000E+21
367  traj.phase0.states:m_50               c    -1.000000E+21     4.995303E+04     1.000000E+21
368  traj.phase0.states:m_51               c    -1.000000E+21     4.995303E+04     1.000000E+21
369  traj.phase0.states:m_52               c    -1.000000E+21     4.995175E+04     1.000000E+21
370  traj.phase0.states:m_53               c    -1.000000E+21     4.994998E+04     1.000000E+21
371  traj.phase0.states:m_54               c    -1.000000E+21     4.994942E+04     1.000000E+21
372  traj.phase0.states:m_55               c    -1.000000E+21     4.994942E+04     1.000000E+21
373  traj.phase0.states:m_56               c    -1.000000E+21     4.994814E+04     1.000000E+21
374  traj.phase0.states:m_57               c    -1.000000E+21     4.994637E+04     1.000000E+21
375  traj.phase0.states:m_58               c    -1.000000E+21     4.994581E+04     1.000000E+21
376  traj.phase0.states:m_59               c    -1.000000E+21     4.994581E+04     1.000000E+21
377  traj.phase0.states:m_60               c    -1.000000E+21     4.994452E+04     1.000000E+21
378  traj.phase0.states:m_61               c    -1.000000E+21     4.994275E+04     1.000000E+21
379  traj.phase0.states:m_62               c    -1.000000E+21     4.994219E+04     1.000000E+21
380  traj.phase0.states:m_63               c    -1.000000E+21     4.994219E+04     1.000000E+21
381  traj.phase0.states:m_64               c    -1.000000E+21     4.994091E+04     1.000000E+21
382  traj.phase0.states:m_65               c    -1.000000E+21     4.993914E+04     1.000000E+21
383  traj.phase0.states:m_66               c    -1.000000E+21     4.993858E+04     1.000000E+21
384  traj.phase0.states:m_67               c    -1.000000E+21     4.993858E+04     1.000000E+21
385  traj.phase0.states:m_68               c    -1.000000E+21     4.993730E+04     1.000000E+21
386  traj.phase0.states:m_69               c    -1.000000E+21     4.993553E+04     1.000000E+21
387  traj.phase0.states:m_70               c    -1.000000E+21     4.993497E+04     1.000000E+21
388  traj.phase0.states:m_71               c    -1.000000E+21     4.993497E+04     1.000000E+21
389  traj.phase0.states:m_72               c    -1.000000E+21     4.993369E+04     1.000000E+21
390  traj.phase0.states:m_73               c    -1.000000E+21     4.993192E+04     1.000000E+21
391  traj.phase0.states:m_74               c    -1.000000E+21     4.993136E+04     1.000000E+21
392  traj.phase0.states:m_75               c    -1.000000E+21     4.993136E+04     1.000000E+21
393  traj.phase0.states:m_76               c    -1.000000E+21     4.993007E+04     1.000000E+21
394  traj.phase0.states:m_77               c    -1.000000E+21     4.992830E+04     1.000000E+21
395  traj.phase0.states:m_78               c    -1.000000E+21     4.992774E+04     1.000000E+21
396  traj.phase0.controls:tan_theta_0      c    -1.000000E+21     2.747399E+00     1.000000E+21
397  traj.phase0.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    0.000000E+00    0.000000E+00              9.00000E+100
3  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
4  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    4.278505E-14    0.000000E+00              9.00000E+100
5  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
6  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    3.422804E-13    0.000000E+00              9.00000E+100
7  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -2.567103E-13    0.000000E+00              9.00000E+100
8  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
9  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -1.711402E-13    0.000000E+00              9.00000E+100
10  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.026841E-12    0.000000E+00              9.00000E+100
11  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.540262E-12    0.000000E+00              9.00000E+100
12  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -1.711402E-12    0.000000E+00              9.00000E+100
13  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -2.053682E-12    0.000000E+00              9.00000E+100
14  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    4.449645E-12    0.000000E+00              9.00000E+100
15  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -7.872448E-12    0.000000E+00              9.00000E+100
16  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -2.738243E-12    0.000000E+00              9.00000E+100
17  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    3.765084E-12    0.000000E+00              9.00000E+100
18  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -1.163753E-11    0.000000E+00              9.00000E+100
19  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    2.053682E-12    0.000000E+00              9.00000E+100
20  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.369121E-12    0.000000E+00              9.00000E+100
21  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -1.848314E-11    0.000000E+00              9.00000E+100
22  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -6.161047E-12    0.000000E+00              9.00000E+100
23  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.300665E-11    0.000000E+00              9.00000E+100
24  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.369121E-12    0.000000E+00              9.00000E+100
25  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -2.053682E-12    0.000000E+00              9.00000E+100
26  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -4.791925E-12    0.000000E+00              9.00000E+100
27  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -2.190594E-11    0.000000E+00              9.00000E+100
28  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -6.845607E-13    0.000000E+00              9.00000E+100
29  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.369121E-12    0.000000E+00              9.00000E+100
30  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.369121E-11    0.000000E+00              9.00000E+100
31  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    4.107364E-12    0.000000E+00              9.00000E+100
32  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    6.845607E-12    0.000000E+00              9.00000E+100
33  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -1.232209E-11    0.000000E+00              9.00000E+100
34  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -1.916770E-11    0.000000E+00              9.00000E+100
35  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    5.476486E-12    0.000000E+00              9.00000E+100
36  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -8.214729E-12    0.000000E+00              9.00000E+100
37  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.779858E-11    0.000000E+00              9.00000E+100
38  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -3.285892E-11    0.000000E+00              9.00000E+100
39  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -5.887222E-11    0.000000E+00              9.00000E+100
40  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.369121E-12    0.000000E+00              9.00000E+100
41  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -1.369121E-12    0.000000E+00              9.00000E+100
42  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    8.214729E-12    0.000000E+00              9.00000E+100
43  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    5.887222E-11    0.000000E+00              9.00000E+100
44  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    7.119432E-11    0.000000E+00              9.00000E+100
45  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    3.012067E-11    0.000000E+00              9.00000E+100
46  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    8.214729E-12    0.000000E+00              9.00000E+100
47  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.095297E-11    0.000000E+00              9.00000E+100
48  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    4.381189E-11    0.000000E+00              9.00000E+100
49  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -3.833540E-11    0.000000E+00              9.00000E+100
50  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -1.095297E-11    0.000000E+00              9.00000E+100
51  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.177444E-10    0.000000E+00              9.00000E+100
52  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -8.214729E-12    0.000000E+00              9.00000E+100
53  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -1.369121E-11    0.000000E+00              9.00000E+100
54  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -4.655013E-11    0.000000E+00              9.00000E+100
55  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.916770E-11    0.000000E+00              9.00000E+100
56  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -6.024134E-11    0.000000E+00              9.00000E+100
57  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    1.807240E-10    0.000000E+00              9.00000E+100
58  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -1.369121E-11    0.000000E+00              9.00000E+100
59  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00    8.214729E-12    0.000000E+00              9.00000E+100
60  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -1.588181E-10    0.000000E+00              9.00000E+100
61  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -5.476486E-12    0.000000E+00              9.00000E+100
62  traj.phase0.collocation_constraint.defects:x         e   0.000000E+00   -5.476486E-12    0.000000E+00              9.00000E+100
63  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    9.176232E-14    0.000000E+00              9.00000E+100
64  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -1.283551E-13    0.000000E+00              9.00000E+100
65  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -8.557009E-14    0.000000E+00              9.00000E+100
66  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    3.422804E-13    0.000000E+00              9.00000E+100
67  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -1.711402E-13    0.000000E+00              9.00000E+100
68  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    6.845607E-13    0.000000E+00              9.00000E+100
69  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    2.395963E-12    0.000000E+00              9.00000E+100
70  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    1.369121E-12    0.000000E+00              9.00000E+100
71  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -3.422804E-13    0.000000E+00              9.00000E+100
72  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    1.369121E-12    0.000000E+00              9.00000E+100
73  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
74  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    4.107364E-12    0.000000E+00              9.00000E+100
75  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -1.163753E-11    0.000000E+00              9.00000E+100
76  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    3.422804E-12    0.000000E+00              9.00000E+100
77  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -1.369121E-12    0.000000E+00              9.00000E+100
78  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -1.026841E-11    0.000000E+00              9.00000E+100
79  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -1.369121E-12    0.000000E+00              9.00000E+100
80  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    6.845607E-13    0.000000E+00              9.00000E+100
81  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -8.899290E-12    0.000000E+00              9.00000E+100
82  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    3.422804E-12    0.000000E+00              9.00000E+100
83  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -2.053682E-11    0.000000E+00              9.00000E+100
84  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    4.791925E-11    0.000000E+00              9.00000E+100
85  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -4.107364E-12    0.000000E+00              9.00000E+100
86  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    2.053682E-12    0.000000E+00              9.00000E+100
87  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -1.642946E-11    0.000000E+00              9.00000E+100
88  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -1.369121E-12    0.000000E+00              9.00000E+100
89  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    6.845607E-12    0.000000E+00              9.00000E+100
90  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -3.148979E-11    0.000000E+00              9.00000E+100
91  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -2.601331E-11    0.000000E+00              9.00000E+100
92  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
93  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    1.369121E-12    0.000000E+00              9.00000E+100
94  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -1.095297E-11    0.000000E+00              9.00000E+100
95  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    1.506034E-11    0.000000E+00              9.00000E+100
96  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    1.369121E-12    0.000000E+00              9.00000E+100
97  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    1.095297E-11    0.000000E+00              9.00000E+100
98  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    1.369121E-11    0.000000E+00              9.00000E+100
99  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00   -1.506034E-11    0.000000E+00              9.00000E+100
100  traj.phase0.collocation_constraint.defects:y         e   0.000000E+00    9.583850E-12    0.000000E+00              9.00000E+100
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254  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.512586E-12    0.000000E+00              9.00000E+100
255  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -2.006452E-11    0.000000E+00              9.00000E+100
256  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    1.631548E-11    0.000000E+00              9.00000E+100
257  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.512586E-12    0.000000E+00              9.00000E+100
258  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -2.006251E-11    0.000000E+00              9.00000E+100
259  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    1.765217E-12    0.000000E+00              9.00000E+100
260  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.041349E-12    0.000000E+00              9.00000E+100
261  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.039344E-12    0.000000E+00              9.00000E+100
262  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    1.763546E-12    0.000000E+00              9.00000E+100
263  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.512586E-12    0.000000E+00              9.00000E+100
264  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.512586E-12    0.000000E+00              9.00000E+100
265  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.039344E-12    0.000000E+00              9.00000E+100
266  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.512586E-12    0.000000E+00              9.00000E+100
267  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.512586E-12    0.000000E+00              9.00000E+100
268  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    1.631548E-11    0.000000E+00              9.00000E+100
269  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -2.006452E-11    0.000000E+00              9.00000E+100
270  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.039344E-12    0.000000E+00              9.00000E+100
271  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    1.763546E-12    0.000000E+00              9.00000E+100
272  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.039344E-12    0.000000E+00              9.00000E+100
273  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    3.814521E-11    0.000000E+00              9.00000E+100
274  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    1.765217E-12    0.000000E+00              9.00000E+100
275  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.510580E-12    0.000000E+00              9.00000E+100
276  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -2.006251E-11    0.000000E+00              9.00000E+100
277  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.510580E-12    0.000000E+00              9.00000E+100
278  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -2.006251E-11    0.000000E+00              9.00000E+100
279  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.037338E-12    0.000000E+00              9.00000E+100
280  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -1.279072E-11    0.000000E+00              9.00000E+100
281  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.037338E-12    0.000000E+00              9.00000E+100
282  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    2.359328E-11    0.000000E+00              9.00000E+100
283  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    1.765217E-12    0.000000E+00              9.00000E+100
284  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.041349E-12    0.000000E+00              9.00000E+100
285  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -2.006652E-11    0.000000E+00              9.00000E+100
286  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    1.761206E-12    0.000000E+00              9.00000E+100
287  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.514591E-12    0.000000E+00              9.00000E+100
288  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -3.461444E-11    0.000000E+00              9.00000E+100
289  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.041349E-12    0.000000E+00              9.00000E+100
290  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.510580E-12    0.000000E+00              9.00000E+100
291  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.041349E-12    0.000000E+00              9.00000E+100
292  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    1.765217E-12    0.000000E+00              9.00000E+100
293  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.041349E-12    0.000000E+00              9.00000E+100
294  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.037338E-12    0.000000E+00              9.00000E+100
295  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.514591E-12    0.000000E+00              9.00000E+100
296  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.037338E-12    0.000000E+00              9.00000E+100
297  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -3.461444E-11    0.000000E+00              9.00000E+100
298  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    1.765217E-12    0.000000E+00              9.00000E+100
299  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -5.510580E-12    0.000000E+00              9.00000E+100
300  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    9.037338E-12    0.000000E+00              9.00000E+100
301  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00    1.761206E-12    0.000000E+00              9.00000E+100
302  traj.phase0.collocation_constraint.defects:m         e   0.000000E+00   -2.006652E-11    0.000000E+00              9.00000E+100
303  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
304  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
305  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
306  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
307  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
308  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
309  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
310  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
311  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
312  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
313  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
314  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
315  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
316  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
317  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
318  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
319  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
320  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
321  traj.phase0.continuity_comp.defect_states:x          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
322  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
323  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
324  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
325  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
326  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
327  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
328  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
329  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
330  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
331  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
332  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
333  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
334  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
335  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
336  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
337  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
338  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
339  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
340  traj.phase0.continuity_comp.defect_states:y          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
341  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
342  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
343  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
344  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
345  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
346  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
347  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
348  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
349  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
350  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
351  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
352  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
353  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
354  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
355  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
356  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
357  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
358  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
359  traj.phase0.continuity_comp.defect_states:vx         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
360  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
361  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
362  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
363  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
364  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
365  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
366  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
367  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
368  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
369  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
370  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
371  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
372  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
373  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
374  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
375  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
376  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
377  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
378  traj.phase0.continuity_comp.defect_states:vy         e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
379  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
380  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
381  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
382  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
383  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
384  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
385  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
386  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
387  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
388  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
389  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
390  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
391  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
392  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
393  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
394  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
395  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
396  traj.phase0.continuity_comp.defect_states:m          e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
397  traj.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/python3.11/site-packages/openmdao/visualization/opt_report/opt_report.py:625: UserWarning: Attempting to set identical low and high ylims makes transformation singular; automatically expanding.
ax.set_ylim([ymin_plot, ymax_plot])
/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/group.py:1098: DerivativesWarning:Constraints or objectives [ode_eval.control_interp.control_rates:tan_theta_rate2] cannot be impacted by the design variables of the problem because no partials were defined for them in their parent component(s).
Simulating trajectory traj
Model viewer data has already been recorded for Driver.
Done simulating trajectory traj
Problem: problem
Driver:  pyOptSparseDriver
success     : True
iterations  : 8
runtime     : 2.5651E+00 s
model_evals : 8
model_time  : 9.0057E-03 s
deriv_evals : 7
deriv_time  : 9.0520E-02 s
exit_status : SUCCESS

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

traj_ax.plot(sim.get_val('traj.phase0.timeseries.x'),
sim.get_val('traj.phase0.timeseries.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.tan_theta')
tan_theta_sim = sim.get_val('traj.phase0.timeseries.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()