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_control('tan_theta', order=1, units=None, opt=True,
                             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'])
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.
#
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
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
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 0.12479484200002844 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:   0.1248 sec
Time to compute coloring:   0.2658 sec
Memory to compute coloring:   0.5000 MB
Coloring created on: 2024-11-23 14:40:04
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
    Objective Function: _objfunc

    Solution: 
--------------------------------------------------------------------------------
    Total Time:                    1.9868
       User Objective Time :       0.0092
       User Sensitivity Time :     1.0055
       Interface Time :            0.0334
       Opt Solver Time:            0.9387
    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           
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        295  traj.phase0.states:vy_57              c    -1.000000E+21     5.355666E+02     1.000000E+21           
        296  traj.phase0.states:vy_58              c    -1.000000E+21     5.254907E+02     1.000000E+21           
        297  traj.phase0.states:vy_59              c    -1.000000E+21     5.254907E+02     1.000000E+21           
        298  traj.phase0.states:vy_60              c    -1.000000E+21     5.005069E+02     1.000000E+21           
        299  traj.phase0.states:vy_61              c    -1.000000E+21     4.618879E+02     1.000000E+21           
        300  traj.phase0.states:vy_62              c    -1.000000E+21     4.487218E+02     1.000000E+21           
        301  traj.phase0.states:vy_63              c    -1.000000E+21     4.487218E+02     1.000000E+21           
        302  traj.phase0.states:vy_64              c    -1.000000E+21     4.169867E+02     1.000000E+21           
        303  traj.phase0.states:vy_65              c    -1.000000E+21     3.698427E+02     1.000000E+21           
        304  traj.phase0.states:vy_66              c    -1.000000E+21     3.541771E+02     1.000000E+21           
        305  traj.phase0.states:vy_67              c    -1.000000E+21     3.541771E+02     1.000000E+21           
        306  traj.phase0.states:vy_68              c    -1.000000E+21     3.170705E+02     1.000000E+21           
        307  traj.phase0.states:vy_69              c    -1.000000E+21     2.632979E+02     1.000000E+21           
        308  traj.phase0.states:vy_70              c    -1.000000E+21     2.457161E+02     1.000000E+21           
        309  traj.phase0.states:vy_71              c    -1.000000E+21     2.457161E+02     1.000000E+21           
        310  traj.phase0.states:vy_72              c    -1.000000E+21     2.045276E+02     1.000000E+21           
        311  traj.phase0.states:vy_73              c    -1.000000E+21     1.457738E+02     1.000000E+21           
        312  traj.phase0.states:vy_74              c    -1.000000E+21     1.267600E+02     1.000000E+21           
        313  traj.phase0.states:vy_75              c    -1.000000E+21     1.267600E+02     1.000000E+21           
        314  traj.phase0.states:vy_76              c    -1.000000E+21     8.253103E+01     1.000000E+21           
        315  traj.phase0.states:vy_77              c    -1.000000E+21     2.007713E+01     1.000000E+21           
        316  traj.phase0.states:vy_78              c    -1.000000E+21     0.000000E+00     1.000000E+21           
        317  traj.phase0.states:m_0                c    -1.000000E+21     4.999872E+04     1.000000E+21           
        318  traj.phase0.states:m_1                c    -1.000000E+21     4.999695E+04     1.000000E+21           
        319  traj.phase0.states:m_2                c    -1.000000E+21     4.999639E+04     1.000000E+21           
        320  traj.phase0.states:m_3                c    -1.000000E+21     4.999639E+04     1.000000E+21           
        321  traj.phase0.states:m_4                c    -1.000000E+21     4.999510E+04     1.000000E+21           
        322  traj.phase0.states:m_5                c    -1.000000E+21     4.999333E+04     1.000000E+21           
        323  traj.phase0.states:m_6                c    -1.000000E+21     4.999277E+04     1.000000E+21           
        324  traj.phase0.states:m_7                c    -1.000000E+21     4.999277E+04     1.000000E+21           
        325  traj.phase0.states:m_8                c    -1.000000E+21     4.999149E+04     1.000000E+21           
        326  traj.phase0.states:m_9                c    -1.000000E+21     4.998972E+04     1.000000E+21           
        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
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        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:1137: DerivativesWarning:Constraints or objectives [ode_eval.control_interp.control_rates:tan_theta_rate, ode_eval.control_interp.control_rates:tan_theta_rate2, ode_eval.control_interp.control_values:tan_theta] 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     : 2.4678E+00 s
  model_evals : 8
  model_time  : 8.1378E-03 s
  deriv_evals : 6
  deriv_time  : 7.8397E-02 s
  exit_status : SUCCESS
sol = om.CaseReader(p.get_outputs_dir() / 'dymos_solution.db').get_case('final')
sim = om.CaseReader(traj.sim_prob.get_outputs_dir() / '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.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()
../../_images/4bceb4a13a05403dc64bc2f4c9a0e81b11503e5257ba2e89c048baff31e1916c.png