# Supersonic Interceptor Minimum Time Climb#

This example is based on the A/C Min Time to Climb example given in chapter 4 of Bryson [Bry99]. It finds the angle-of-attack history required to accelerate a supersonic interceptor from near ground level, Mach 0.4 to an altitude of 20 km and Mach 1.0.

The vehicle dynamics are given by

(62)#\begin{align} \frac{dv}{dt} &= \frac{T}{m} \cos \alpha - \frac{D}{m} - g \sin \gamma \\ \frac{d\gamma}{dt} &= \frac{T}{m v} \sin \alpha + \frac{L}{m v} - \frac{g \cos \gamma}{v} \\ \frac{dh}{dt} &= v \sin \gamma \\ \frac{dr}{dt} &= v \cos \gamma \\ \frac{dm}{dt} &= - \frac{T}{g I_{sp}} \end{align}

The initial conditions are

(63)#\begin{align} r_0 &= 0 \rm{\,m} \\ h_0 &= 100 \rm{\,m} \\ v_0 &= 135.964 \rm{\,m/s} \\ \gamma_0 &= 0 \rm{\,deg} \\ m_0 &= 19030.468 \rm{\,kg} \end{align}

and the final conditions are

(64)#\begin{align} h_f &= 20000 \rm{\,m} \\ M_f &= 1.0 \\ \gamma_0 &= 0 \rm{\,deg} \end{align}

## The ODE System: min_time_climb_ode.py#

The top level ODE definition is a Group that connects several subsystems.

Hide code cell outputs
import openmdao.api as om
from .dynamic_pressure_comp_partial_coloring import DynamicPressureCompFD
from ..aero.dynamic_pressure_comp import DynamicPressureComp
from ..aero.lift_drag_force_comp import LiftDragForceComp
from ..aero.cd0_comp import CD0Comp
from ..aero.kappa_comp import KappaComp
from ..aero.cla_comp import CLaComp
from ..aero.cl_comp import CLComp
from ..aero.cd_comp import CDComp
from ..aero.mach_comp import MachComp

class AeroGroup(om.Group):
"""
The purpose of the AeroGroup is to compute the aerodynamic forces on the
aircraft in the body frame.

Parameters
----------
v : float
air-relative velocity (m/s)
sos : float
local speed of sound (m/s)
rho : float
atmospheric density (kg/m**3)
alpha : float
S : float
aerodynamic reference area (m**2)

"""
def initialize(self):
self.options.declare('num_nodes', types=int,
desc='Number of nodes to be evaluated in the RHS')
self.options.declare('fd', types=bool, default=False, desc='If True, use fd for partials for dynamic pressure')
self.options.declare('partial_coloring', types=bool, default=False,
desc='If True and fd is True, color the approximated partials of dynamic pressure')

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

if self.options['fd']:
q_comp = DynamicPressureCompFD(num_nodes=nn, partial_coloring=self.options['partial_coloring'])
else:
q_comp = DynamicPressureComp(num_nodes=nn)

subsys=MachComp(num_nodes=nn),
promotes_inputs=['v', 'sos'],
promotes_outputs=['mach'])

subsys=CD0Comp(num_nodes=nn),
promotes_inputs=['mach'],
promotes_outputs=['CD0'])

subsys=KappaComp(num_nodes=nn),
promotes_inputs=['mach'],
promotes_outputs=['kappa'])

subsys=CLaComp(num_nodes=nn),
promotes_inputs=['mach'],
promotes_outputs=['CLa'])

subsys=CLComp(num_nodes=nn),
promotes_inputs=['alpha', 'CLa'],
promotes_outputs=['CL'])

subsys=CDComp(num_nodes=nn),
promotes_inputs=['CD0', 'alpha', 'CLa', 'kappa'],
promotes_outputs=['CD'])

subsys=q_comp,
promotes_inputs=['rho', 'v'],
promotes_outputs=['q'])

subsys=LiftDragForceComp(num_nodes=nn),
promotes_inputs=['CL', 'CD', 'q', 'S'],
promotes_outputs=['f_lift', 'f_drag'])

import openmdao.api as om
from dymos.models.eom import FlightPathEOM2D
from dymos.examples.min_time_climb.prop import PropGroup
from dymos.models.atmosphere import USatm1976Comp
from dymos.examples.min_time_climb.doc.aero_partial_coloring import AeroGroup

class MinTimeClimbODE(om.Group):

def initialize(self):
self.options.declare('num_nodes', types=int)
self.options.declare('fd', types=bool, default=False, desc='If True, use fd for partials')
self.options.declare('partial_coloring', types=bool, default=False,
desc='If True and fd is True, color the approximated partials')

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

subsys=USatm1976Comp(num_nodes=nn, h_def='geodetic'),
promotes_inputs=['h'])

subsys=AeroGroup(num_nodes=nn,
fd=self.options['fd'],
partial_coloring=self.options['partial_coloring']),
promotes_inputs=['v', 'alpha', 'S'])

self.connect('atmos.sos', 'aero.sos')
self.connect('atmos.rho', 'aero.rho')

subsys=PropGroup(num_nodes=nn),
promotes_inputs=['h', 'Isp', 'throttle'])

self.connect('aero.mach', 'prop.mach')

subsys=FlightPathEOM2D(num_nodes=nn),
promotes_inputs=['m', 'v', 'gam', 'alpha'])

self.connect('aero.f_drag', 'flight_dynamics.D')
self.connect('aero.f_lift', 'flight_dynamics.L')
self.connect('prop.thrust', 'flight_dynamics.T')


## Building and running the problem#

In the following code we follow the following process to solve the problem:

import matplotlib.pyplot as plt

import openmdao.api as om

import dymos as dm
from dymos.examples.plotting import plot_results

#
# Instantiate the problem and configure the optimization driver
#
p = om.Problem(model=om.Group())

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

#
# Instantiate the trajectory and phase
#
traj = dm.Trajectory()

phase = dm.Phase(ode_class=MinTimeClimbODE,
transcription=dm.GaussLobatto(num_segments=15, compressed=False))

#
# Set the options on the optimization variables
# Note the use of explicit state units here since much of the ODE uses imperial units
# and we prefer to solve this problem using metric units.
#
phase.set_time_options(fix_initial=True, duration_bounds=(50, 400),
duration_ref=100.0)

ref=1.0E3, defect_ref=1.0E3,
rate_source='flight_dynamics.r_dot')

ref=1.0E2, defect_ref=1.0E2,
rate_source='flight_dynamics.h_dot')

ref=1.0E2, defect_ref=1.0E2,
rate_source='flight_dynamics.v_dot')

ref=1.0, defect_ref=1.0,
rate_source='flight_dynamics.gam_dot')

ref=1.0E3, defect_ref=1.0E3,
rate_source='prop.m_dot')

rate_continuity=True, rate_continuity_scaler=100.0,
rate2_continuity=False)

#
# Setup the boundary and path constraints
#

# Minimize time at the end of the phase

p.model.linear_solver = om.DirectSolver()

#
# Setup the problem and set the initial guess
#
p.setup(check=True)

p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 500

p.set_val('traj.phase0.states:r', phase.interp('r', [0.0, 50000.0]))
p.set_val('traj.phase0.states:h', phase.interp('h', [100.0, 20000.0]))
p.set_val('traj.phase0.states:v', phase.interp('v', [135.964, 283.159]))
p.set_val('traj.phase0.states:gam', phase.interp('gam', [0.0, 0.0]))
p.set_val('traj.phase0.states:m', phase.interp('m', [19030.468, 10000.]))
p.set_val('traj.phase0.controls:alpha', phase.interp('alpha', [0.0, 0.0]))

#
# Solve for the optimal trajectory
#
dm.run_problem(p, simulate=True)

--- Constraint Report [traj] ---
--- phase0 ---
[final]   2.0000e+04 == h [m]
[final]   1.0000e+00 == aero.mach [None]
[path]    1.0000e+02 <= h <= 2.0000e+04  [m]
[path]    1.0000e-01 <= aero.mach <= 1.8000e+00  [None]

INFO: checking out_of_order

INFO:check_config:checking out_of_order

INFO: checking system

INFO:check_config:checking system

INFO: checking solvers

INFO:check_config:checking solvers

INFO: checking dup_inputs

INFO:check_config:checking dup_inputs

INFO: checking missing_recorders

INFO:check_config:checking missing_recorders

WARNING: The Problem has no recorder of any kind attached

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

INFO: checking unserializable_options

INFO:check_config:checking unserializable_options

INFO: checking comp_has_no_outputs

INFO:check_config:checking comp_has_no_outputs

INFO: checking auto_ivc_warnings

INFO:check_config:checking auto_ivc_warnings

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

INFO:check_config:checking out_of_order

INFO: checking system

INFO:check_config:checking system

INFO: checking solvers

INFO:check_config:checking solvers

INFO: checking dup_inputs

INFO:check_config:checking dup_inputs

INFO: checking missing_recorders

INFO:check_config:checking missing_recorders

WARNING: The Problem has no recorder of any kind attached

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

INFO: checking unserializable_options

INFO:check_config:checking unserializable_options

INFO: checking comp_has_no_outputs

INFO:check_config:checking comp_has_no_outputs

INFO: checking auto_ivc_warnings

INFO:check_config:checking auto_ivc_warnings

/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/driver.py:469: DriverWarning:The following design variable initial conditions are out of their specified bounds:
traj.phase0.t_duration
val: [500.]
lower: 50.0
upper: 400.0
Set the initial value of the design variable to a valid value or set the driver option['invalid_desvar_behavior'] to 'ignore'.

Full total jacobian was computed 3 times, taking 0.156272 seconds.
Total jacobian shape: (181, 191)

Jacobian shape: (181, 191)  ( 5.29% nonzero)
FWD solves: 1   REV solves: 12
Total colors vs. total size: 13 vs 181  (92.8% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.156272 sec.
Time to compute coloring: 0.166290 sec.
Memory to compute coloring: 0.250000 MB.

/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/total_jac.py:1782: DerivativesWarning:Constraints or objectives [('traj.phases.phase0.timeseries.timeseries_comp.h', inds=[(0, 0)]), ('traj.phases.phase0.timeseries.timeseries_comp.mach', inds=[(0, 0)])] cannot be impacted by the design variables of the problem.

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

Solution:
--------------------------------------------------------------------------------
Total Time:                    7.4685
User Objective Time :       1.4850
User Sensitivity Time :     1.1193
Interface Time :            0.9049
Opt Solver Time:            3.9593
Calls to Objective Function :     131
Calls to Sens Function :          108

Objectives
Index  Name                                 Value
0  traj.phases.phase0.time.t     3.252582E+02

Variables (c - continuous, i - integer, d - discrete)
Index  Name                                                                Type      Lower Bound            Value      Upper Bound     Status
0  traj.phase0.t_duration_0                                               c     5.000000E-01     3.252582E+00     4.000000E+00
1  traj.phases.phase0.indep_states.states:r_0                             c     0.000000E+00     4.337701E+00     1.000000E+03
2  traj.phases.phase0.indep_states.states:r_1                             c     0.000000E+00     4.337701E+00     1.000000E+03
3  traj.phases.phase0.indep_states.states:r_2                             c     0.000000E+00     1.031226E+01     1.000000E+03
4  traj.phases.phase0.indep_states.states:r_3                             c     0.000000E+00     1.031226E+01     1.000000E+03
5  traj.phases.phase0.indep_states.states:r_4                             c     0.000000E+00     1.587301E+01     1.000000E+03
6  traj.phases.phase0.indep_states.states:r_5                             c     0.000000E+00     1.587301E+01     1.000000E+03
7  traj.phases.phase0.indep_states.states:r_6                             c     0.000000E+00     2.161347E+01     1.000000E+03
8  traj.phases.phase0.indep_states.states:r_7                             c     0.000000E+00     2.161347E+01     1.000000E+03
9  traj.phases.phase0.indep_states.states:r_8                             c     0.000000E+00     2.800905E+01     1.000000E+03
10  traj.phases.phase0.indep_states.states:r_9                             c     0.000000E+00     2.800905E+01     1.000000E+03
11  traj.phases.phase0.indep_states.states:r_10                            c     0.000000E+00     3.569474E+01     1.000000E+03
12  traj.phases.phase0.indep_states.states:r_11                            c     0.000000E+00     3.569474E+01     1.000000E+03
13  traj.phases.phase0.indep_states.states:r_12                            c     0.000000E+00     4.461505E+01     1.000000E+03
14  traj.phases.phase0.indep_states.states:r_13                            c     0.000000E+00     4.461505E+01     1.000000E+03
15  traj.phases.phase0.indep_states.states:r_14                            c     0.000000E+00     5.396432E+01     1.000000E+03
16  traj.phases.phase0.indep_states.states:r_15                            c     0.000000E+00     5.396432E+01     1.000000E+03
17  traj.phases.phase0.indep_states.states:r_16                            c     0.000000E+00     6.365832E+01     1.000000E+03
18  traj.phases.phase0.indep_states.states:r_17                            c     0.000000E+00     6.365832E+01     1.000000E+03
19  traj.phases.phase0.indep_states.states:r_18                            c     0.000000E+00     7.372149E+01     1.000000E+03
20  traj.phases.phase0.indep_states.states:r_19                            c     0.000000E+00     7.372149E+01     1.000000E+03
21  traj.phases.phase0.indep_states.states:r_20                            c     0.000000E+00     8.422514E+01     1.000000E+03
22  traj.phases.phase0.indep_states.states:r_21                            c     0.000000E+00     8.422514E+01     1.000000E+03
23  traj.phases.phase0.indep_states.states:r_22                            c     0.000000E+00     9.527718E+01     1.000000E+03
24  traj.phases.phase0.indep_states.states:r_23                            c     0.000000E+00     9.527718E+01     1.000000E+03
25  traj.phases.phase0.indep_states.states:r_24                            c     0.000000E+00     1.058978E+02     1.000000E+03
26  traj.phases.phase0.indep_states.states:r_25                            c     0.000000E+00     1.058978E+02     1.000000E+03
27  traj.phases.phase0.indep_states.states:r_26                            c     0.000000E+00     1.136083E+02     1.000000E+03
28  traj.phases.phase0.indep_states.states:r_27                            c     0.000000E+00     1.136083E+02     1.000000E+03
29  traj.phases.phase0.indep_states.states:r_28                            c     0.000000E+00     1.199394E+02     1.000000E+03
30  traj.phases.phase0.indep_states.states:h_0                             c     0.000000E+00     2.446232E+00     2.000000E+02
31  traj.phases.phase0.indep_states.states:h_1                             c     0.000000E+00     2.446232E+00     2.000000E+02
32  traj.phases.phase0.indep_states.states:h_2                             c     0.000000E+00     2.523425E+01     2.000000E+02
33  traj.phases.phase0.indep_states.states:h_3                             c     0.000000E+00     2.523425E+01     2.000000E+02
34  traj.phases.phase0.indep_states.states:h_4                             c     0.000000E+00     5.979155E+01     2.000000E+02
35  traj.phases.phase0.indep_states.states:h_5                             c     0.000000E+00     5.979155E+01     2.000000E+02
36  traj.phases.phase0.indep_states.states:h_6                             c     0.000000E+00     8.468632E+01     2.000000E+02
37  traj.phases.phase0.indep_states.states:h_7                             c     0.000000E+00     8.468632E+01     2.000000E+02
38  traj.phases.phase0.indep_states.states:h_8                             c     0.000000E+00     8.839941E+01     2.000000E+02
39  traj.phases.phase0.indep_states.states:h_9                             c     0.000000E+00     8.839941E+01     2.000000E+02
40  traj.phases.phase0.indep_states.states:h_10                            c     0.000000E+00     7.334356E+01     2.000000E+02
41  traj.phases.phase0.indep_states.states:h_11                            c     0.000000E+00     7.334356E+01     2.000000E+02
42  traj.phases.phase0.indep_states.states:h_12                            c     0.000000E+00     7.147458E+01     2.000000E+02
43  traj.phases.phase0.indep_states.states:h_13                            c     0.000000E+00     7.147458E+01     2.000000E+02
44  traj.phases.phase0.indep_states.states:h_14                            c     0.000000E+00     7.715270E+01     2.000000E+02
45  traj.phases.phase0.indep_states.states:h_15                            c     0.000000E+00     7.715270E+01     2.000000E+02
46  traj.phases.phase0.indep_states.states:h_16                            c     0.000000E+00     8.262303E+01     2.000000E+02
47  traj.phases.phase0.indep_states.states:h_17                            c     0.000000E+00     8.262303E+01     2.000000E+02
48  traj.phases.phase0.indep_states.states:h_18                            c     0.000000E+00     8.815355E+01     2.000000E+02
49  traj.phases.phase0.indep_states.states:h_19                            c     0.000000E+00     8.815355E+01     2.000000E+02
50  traj.phases.phase0.indep_states.states:h_20                            c     0.000000E+00     9.138943E+01     2.000000E+02
51  traj.phases.phase0.indep_states.states:h_21                            c     0.000000E+00     9.138943E+01     2.000000E+02
52  traj.phases.phase0.indep_states.states:h_22                            c     0.000000E+00     9.362154E+01     2.000000E+02
53  traj.phases.phase0.indep_states.states:h_23                            c     0.000000E+00     9.362154E+01     2.000000E+02
54  traj.phases.phase0.indep_states.states:h_24                            c     0.000000E+00     1.207562E+02     2.000000E+02
55  traj.phases.phase0.indep_states.states:h_25                            c     0.000000E+00     1.207562E+02     2.000000E+02
56  traj.phases.phase0.indep_states.states:h_26                            c     0.000000E+00     1.726212E+02     2.000000E+02
57  traj.phases.phase0.indep_states.states:h_27                            c     0.000000E+00     1.726212E+02     2.000000E+02
58  traj.phases.phase0.indep_states.states:h_28                            c     0.000000E+00     2.000000E+02     2.000000E+02          u
59  traj.phases.phase0.indep_states.states:v_0                             c     1.000000E-01     2.633872E+00     1.000000E+19
60  traj.phases.phase0.indep_states.states:v_1                             c     1.000000E-01     2.633872E+00     1.000000E+19
61  traj.phases.phase0.indep_states.states:v_2                             c     1.000000E-01     3.104846E+00     1.000000E+19
62  traj.phases.phase0.indep_states.states:v_3                             c     1.000000E-01     3.104846E+00     1.000000E+19
63  traj.phases.phase0.indep_states.states:v_4                             c     1.000000E-01     2.949267E+00     1.000000E+19
64  traj.phases.phase0.indep_states.states:v_5                             c     1.000000E-01     2.949267E+00     1.000000E+19
65  traj.phases.phase0.indep_states.states:v_6                             c     1.000000E-01     2.842952E+00     1.000000E+19
66  traj.phases.phase0.indep_states.states:v_7                             c     1.000000E-01     2.842952E+00     1.000000E+19
67  traj.phases.phase0.indep_states.states:v_8                             c     1.000000E-01     3.249032E+00     1.000000E+19
68  traj.phases.phase0.indep_states.states:v_9                             c     1.000000E-01     3.249032E+00     1.000000E+19
69  traj.phases.phase0.indep_states.states:v_10                            c     1.000000E-01     3.941138E+00     1.000000E+19
70  traj.phases.phase0.indep_states.states:v_11                            c     1.000000E-01     3.941138E+00     1.000000E+19
71  traj.phases.phase0.indep_states.states:v_12                            c     1.000000E-01     4.243012E+00     1.000000E+19
72  traj.phases.phase0.indep_states.states:v_13                            c     1.000000E-01     4.243012E+00     1.000000E+19
73  traj.phases.phase0.indep_states.states:v_14                            c     1.000000E-01     4.394793E+00     1.000000E+19
74  traj.phases.phase0.indep_states.states:v_15                            c     1.000000E-01     4.394793E+00     1.000000E+19
75  traj.phases.phase0.indep_states.states:v_16                            c     1.000000E-01     4.562262E+00     1.000000E+19
76  traj.phases.phase0.indep_states.states:v_17                            c     1.000000E-01     4.562262E+00     1.000000E+19
77  traj.phases.phase0.indep_states.states:v_18                            c     1.000000E-01     4.737102E+00     1.000000E+19
78  traj.phases.phase0.indep_states.states:v_19                            c     1.000000E-01     4.737102E+00     1.000000E+19
79  traj.phases.phase0.indep_states.states:v_20                            c     1.000000E-01     4.969617E+00     1.000000E+19
80  traj.phases.phase0.indep_states.states:v_21                            c     1.000000E-01     4.969617E+00     1.000000E+19
81  traj.phases.phase0.indep_states.states:v_22                            c     1.000000E-01     5.193973E+00     1.000000E+19
82  traj.phases.phase0.indep_states.states:v_23                            c     1.000000E-01     5.193973E+00     1.000000E+19
83  traj.phases.phase0.indep_states.states:v_24                            c     1.000000E-01     4.826574E+00     1.000000E+19
84  traj.phases.phase0.indep_states.states:v_25                            c     1.000000E-01     4.826574E+00     1.000000E+19
85  traj.phases.phase0.indep_states.states:v_26                            c     1.000000E-01     3.708828E+00     1.000000E+19
86  traj.phases.phase0.indep_states.states:v_27                            c     1.000000E-01     3.708828E+00     1.000000E+19
87  traj.phases.phase0.indep_states.states:v_28                            c     1.000000E-01     2.950719E+00     1.000000E+19
88  traj.phases.phase0.indep_states.states:gam_0                           c    -1.500000E+00     1.014639E-01     1.500000E+00
89  traj.phases.phase0.indep_states.states:gam_1                           c    -1.500000E+00     1.014639E-01     1.500000E+00
90  traj.phases.phase0.indep_states.states:gam_2                           c    -1.500000E+00     5.977726E-01     1.500000E+00
91  traj.phases.phase0.indep_states.states:gam_3                           c    -1.500000E+00     5.977726E-01     1.500000E+00
92  traj.phases.phase0.indep_states.states:gam_4                           c    -1.500000E+00     4.558137E-01     1.500000E+00
93  traj.phases.phase0.indep_states.states:gam_5                           c    -1.500000E+00     4.558137E-01     1.500000E+00
94  traj.phases.phase0.indep_states.states:gam_6                           c    -1.500000E+00     3.189616E-01     1.500000E+00
95  traj.phases.phase0.indep_states.states:gam_7                           c    -1.500000E+00     3.189616E-01     1.500000E+00
96  traj.phases.phase0.indep_states.states:gam_8                           c    -1.500000E+00    -1.774494E-01     1.500000E+00
97  traj.phases.phase0.indep_states.states:gam_9                           c    -1.500000E+00    -1.774494E-01     1.500000E+00
98  traj.phases.phase0.indep_states.states:gam_10                          c    -1.500000E+00    -1.196089E-01     1.500000E+00
99  traj.phases.phase0.indep_states.states:gam_11                          c    -1.500000E+00    -1.196089E-01     1.500000E+00
100  traj.phases.phase0.indep_states.states:gam_12                          c    -1.500000E+00     4.700158E-02     1.500000E+00
101  traj.phases.phase0.indep_states.states:gam_13                          c    -1.500000E+00     4.700158E-02     1.500000E+00
102  traj.phases.phase0.indep_states.states:gam_14                          c    -1.500000E+00     5.968499E-02     1.500000E+00
103  traj.phases.phase0.indep_states.states:gam_15                          c    -1.500000E+00     5.968499E-02     1.500000E+00
104  traj.phases.phase0.indep_states.states:gam_16                          c    -1.500000E+00     5.570414E-02     1.500000E+00
105  traj.phases.phase0.indep_states.states:gam_17                          c    -1.500000E+00     5.570414E-02     1.500000E+00
106  traj.phases.phase0.indep_states.states:gam_18                          c    -1.500000E+00     4.944531E-02     1.500000E+00
107  traj.phases.phase0.indep_states.states:gam_19                          c    -1.500000E+00     4.944531E-02     1.500000E+00
108  traj.phases.phase0.indep_states.states:gam_20                          c    -1.500000E+00     1.063244E-02     1.500000E+00
109  traj.phases.phase0.indep_states.states:gam_21                          c    -1.500000E+00     1.063244E-02     1.500000E+00
110  traj.phases.phase0.indep_states.states:gam_22                          c    -1.500000E+00     7.512639E-02     1.500000E+00
111  traj.phases.phase0.indep_states.states:gam_23                          c    -1.500000E+00     7.512639E-02     1.500000E+00
112  traj.phases.phase0.indep_states.states:gam_24                          c    -1.500000E+00     4.620644E-01     1.500000E+00
113  traj.phases.phase0.indep_states.states:gam_25                          c    -1.500000E+00     4.620644E-01     1.500000E+00
114  traj.phases.phase0.indep_states.states:gam_26                          c    -1.500000E+00     6.283511E-01     1.500000E+00
115  traj.phases.phase0.indep_states.states:gam_27                          c    -1.500000E+00     6.283511E-01     1.500000E+00
116  traj.phases.phase0.indep_states.states:gam_28                          c    -1.500000E+00     0.000000E+00     1.500000E+00
117  traj.phases.phase0.indep_states.states:m_0                             c     1.000000E-02     1.883945E+01     1.000000E+02
118  traj.phases.phase0.indep_states.states:m_1                             c     1.000000E-02     1.883945E+01     1.000000E+02
119  traj.phases.phase0.indep_states.states:m_2                             c     1.000000E-02     1.863480E+01     1.000000E+02
120  traj.phases.phase0.indep_states.states:m_3                             c     1.000000E-02     1.863480E+01     1.000000E+02
121  traj.phases.phase0.indep_states.states:m_4                             c     1.000000E-02     1.847306E+01     1.000000E+02
122  traj.phases.phase0.indep_states.states:m_5                             c     1.000000E-02     1.847306E+01     1.000000E+02
123  traj.phases.phase0.indep_states.states:m_6                             c     1.000000E-02     1.835398E+01     1.000000E+02
124  traj.phases.phase0.indep_states.states:m_7                             c     1.000000E-02     1.835398E+01     1.000000E+02
125  traj.phases.phase0.indep_states.states:m_8                             c     1.000000E-02     1.825096E+01     1.000000E+02
126  traj.phases.phase0.indep_states.states:m_9                             c     1.000000E-02     1.825096E+01     1.000000E+02
127  traj.phases.phase0.indep_states.states:m_10                            c     1.000000E-02     1.811453E+01     1.000000E+02
128  traj.phases.phase0.indep_states.states:m_11                            c     1.000000E-02     1.811453E+01     1.000000E+02
129  traj.phases.phase0.indep_states.states:m_12                            c     1.000000E-02     1.794309E+01     1.000000E+02
130  traj.phases.phase0.indep_states.states:m_13                            c     1.000000E-02     1.794309E+01     1.000000E+02
131  traj.phases.phase0.indep_states.states:m_14                            c     1.000000E-02     1.776701E+01     1.000000E+02
132  traj.phases.phase0.indep_states.states:m_15                            c     1.000000E-02     1.776701E+01     1.000000E+02
133  traj.phases.phase0.indep_states.states:m_16                            c     1.000000E-02     1.759238E+01     1.000000E+02
134  traj.phases.phase0.indep_states.states:m_17                            c     1.000000E-02     1.759238E+01     1.000000E+02
135  traj.phases.phase0.indep_states.states:m_18                            c     1.000000E-02     1.741891E+01     1.000000E+02
136  traj.phases.phase0.indep_states.states:m_19                            c     1.000000E-02     1.741891E+01     1.000000E+02
137  traj.phases.phase0.indep_states.states:m_20                            c     1.000000E-02     1.724488E+01     1.000000E+02
138  traj.phases.phase0.indep_states.states:m_21                            c     1.000000E-02     1.724488E+01     1.000000E+02
139  traj.phases.phase0.indep_states.states:m_22                            c     1.000000E-02     1.706474E+01     1.000000E+02
140  traj.phases.phase0.indep_states.states:m_23                            c     1.000000E-02     1.706474E+01     1.000000E+02
141  traj.phases.phase0.indep_states.states:m_24                            c     1.000000E-02     1.690446E+01     1.000000E+02
142  traj.phases.phase0.indep_states.states:m_25                            c     1.000000E-02     1.690446E+01     1.000000E+02
143  traj.phases.phase0.indep_states.states:m_26                            c     1.000000E-02     1.682855E+01     1.000000E+02
144  traj.phases.phase0.indep_states.states:m_27                            c     1.000000E-02     1.682855E+01     1.000000E+02
145  traj.phases.phase0.indep_states.states:m_28                            c     1.000000E-02     1.680500E+01     1.000000E+02
146  traj.phases.phase0.control_group.indep_controls.controls:alpha_0       c    -8.000000E+00     5.400148E+00     8.000000E+00
147  traj.phases.phase0.control_group.indep_controls.controls:alpha_1       c    -8.000000E+00     2.646126E+00     8.000000E+00
148  traj.phases.phase0.control_group.indep_controls.controls:alpha_2       c    -8.000000E+00     2.027074E+00     8.000000E+00
149  traj.phases.phase0.control_group.indep_controls.controls:alpha_3       c    -8.000000E+00     2.027074E+00     8.000000E+00
150  traj.phases.phase0.control_group.indep_controls.controls:alpha_4       c    -8.000000E+00     2.079594E+00     8.000000E+00
151  traj.phases.phase0.control_group.indep_controls.controls:alpha_5       c    -8.000000E+00     1.340289E+00     8.000000E+00
152  traj.phases.phase0.control_group.indep_controls.controls:alpha_6       c    -8.000000E+00     1.340289E+00     8.000000E+00
153  traj.phases.phase0.control_group.indep_controls.controls:alpha_7       c    -8.000000E+00     7.778215E-01     8.000000E+00
154  traj.phases.phase0.control_group.indep_controls.controls:alpha_8       c    -8.000000E+00     1.360854E+00     8.000000E+00
155  traj.phases.phase0.control_group.indep_controls.controls:alpha_9       c    -8.000000E+00     1.360854E+00     8.000000E+00
156  traj.phases.phase0.control_group.indep_controls.controls:alpha_10      c    -8.000000E+00     1.890980E+00     8.000000E+00
157  traj.phases.phase0.control_group.indep_controls.controls:alpha_11      c    -8.000000E+00     1.169794E+00     8.000000E+00
158  traj.phases.phase0.control_group.indep_controls.controls:alpha_12      c    -8.000000E+00     1.169794E+00     8.000000E+00
159  traj.phases.phase0.control_group.indep_controls.controls:alpha_13      c    -8.000000E+00     4.839422E-01     8.000000E+00
160  traj.phases.phase0.control_group.indep_controls.controls:alpha_14      c    -8.000000E+00     1.120071E+00     8.000000E+00
161  traj.phases.phase0.control_group.indep_controls.controls:alpha_15      c    -8.000000E+00     1.120071E+00     8.000000E+00
162  traj.phases.phase0.control_group.indep_controls.controls:alpha_16      c    -8.000000E+00     1.996289E+00     8.000000E+00
163  traj.phases.phase0.control_group.indep_controls.controls:alpha_17      c    -8.000000E+00     2.030702E+00     8.000000E+00
164  traj.phases.phase0.control_group.indep_controls.controls:alpha_18      c    -8.000000E+00     2.030702E+00     8.000000E+00
165  traj.phases.phase0.control_group.indep_controls.controls:alpha_19      c    -8.000000E+00     1.681618E+00     8.000000E+00
166  traj.phases.phase0.control_group.indep_controls.controls:alpha_20      c    -8.000000E+00     1.407344E+00     8.000000E+00
167  traj.phases.phase0.control_group.indep_controls.controls:alpha_21      c    -8.000000E+00     1.407344E+00     8.000000E+00
168  traj.phases.phase0.control_group.indep_controls.controls:alpha_22      c    -8.000000E+00     1.239210E+00     8.000000E+00
169  traj.phases.phase0.control_group.indep_controls.controls:alpha_23      c    -8.000000E+00     1.208547E+00     8.000000E+00
170  traj.phases.phase0.control_group.indep_controls.controls:alpha_24      c    -8.000000E+00     1.208547E+00     8.000000E+00
171  traj.phases.phase0.control_group.indep_controls.controls:alpha_25      c    -8.000000E+00     1.241627E+00     8.000000E+00
172  traj.phases.phase0.control_group.indep_controls.controls:alpha_26      c    -8.000000E+00     1.264724E+00     8.000000E+00
173  traj.phases.phase0.control_group.indep_controls.controls:alpha_27      c    -8.000000E+00     1.264724E+00     8.000000E+00
174  traj.phases.phase0.control_group.indep_controls.controls:alpha_28      c    -8.000000E+00     1.259051E+00     8.000000E+00
175  traj.phases.phase0.control_group.indep_controls.controls:alpha_29      c    -8.000000E+00     1.205824E+00     8.000000E+00
176  traj.phases.phase0.control_group.indep_controls.controls:alpha_30      c    -8.000000E+00     1.205824E+00     8.000000E+00
177  traj.phases.phase0.control_group.indep_controls.controls:alpha_31      c    -8.000000E+00     1.152401E+00     8.000000E+00
178  traj.phases.phase0.control_group.indep_controls.controls:alpha_32      c    -8.000000E+00     1.146142E+00     8.000000E+00
179  traj.phases.phase0.control_group.indep_controls.controls:alpha_33      c    -8.000000E+00     1.146142E+00     8.000000E+00
180  traj.phases.phase0.control_group.indep_controls.controls:alpha_34      c    -8.000000E+00     1.349957E+00     8.000000E+00
181  traj.phases.phase0.control_group.indep_controls.controls:alpha_35      c    -8.000000E+00     1.926759E+00     8.000000E+00
182  traj.phases.phase0.control_group.indep_controls.controls:alpha_36      c    -8.000000E+00     1.926759E+00     8.000000E+00
183  traj.phases.phase0.control_group.indep_controls.controls:alpha_37      c    -8.000000E+00     2.730389E+00     8.000000E+00
184  traj.phases.phase0.control_group.indep_controls.controls:alpha_38      c    -8.000000E+00     3.614690E+00     8.000000E+00
185  traj.phases.phase0.control_group.indep_controls.controls:alpha_39      c    -8.000000E+00     3.614690E+00     8.000000E+00
186  traj.phases.phase0.control_group.indep_controls.controls:alpha_40      c    -8.000000E+00     3.938266E+00     8.000000E+00
187  traj.phases.phase0.control_group.indep_controls.controls:alpha_41      c    -8.000000E+00     3.059725E+00     8.000000E+00
188  traj.phases.phase0.control_group.indep_controls.controls:alpha_42      c    -8.000000E+00     3.059725E+00     8.000000E+00
189  traj.phases.phase0.control_group.indep_controls.controls:alpha_43      c    -8.000000E+00    -9.823039E-02     8.000000E+00
190  traj.phases.phase0.control_group.indep_controls.controls:alpha_44      c    -8.000000E+00    -6.612894E+00     8.000000E+00

Constraints (i - inequality, e - equality)
Index  Name                                                               Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
0  traj.phases.phase0->final_boundary_constraint->h                      e   2.000000E+01    2.000000E+01    2.000000E+01              9.00000E+100
1  traj.phases.phase0->final_boundary_constraint->mach                   e   1.000000E+00    1.000000E+00    1.000000E+00              9.00000E+100
2  traj.phases.phase0->final_boundary_constraint->gam                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
3  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.584610E-10    0.000000E+00              9.00000E+100
4  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00   -2.415992E-11    0.000000E+00              9.00000E+100
5  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    6.957338E-10    0.000000E+00              9.00000E+100
6  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    4.010558E-10    0.000000E+00              9.00000E+100
7  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    3.194947E-09    0.000000E+00              9.00000E+100
8  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    4.847712E-10    0.000000E+00              9.00000E+100
9  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    3.020417E-09    0.000000E+00              9.00000E+100
10  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    2.301440E-09    0.000000E+00              9.00000E+100
11  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    9.152321E-10    0.000000E+00              9.00000E+100
12  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    6.911911E-10    0.000000E+00              9.00000E+100
13  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.937268E-10    0.000000E+00              9.00000E+100
14  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.069336E-10    0.000000E+00              9.00000E+100
15  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00   -2.135147E-11    0.000000E+00              9.00000E+100
16  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    8.720275E-10    0.000000E+00              9.00000E+100
17  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.393685E-10    0.000000E+00              9.00000E+100
18  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    7.098615E-10    0.000000E+00              9.00000E+100
19  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    7.136202E-09    0.000000E+00              9.00000E+100
20  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    5.237505E-10    0.000000E+00              9.00000E+100
21  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.733443E-09    0.000000E+00              9.00000E+100
22  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    4.110918E-08    0.000000E+00              9.00000E+100
23  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.676331E-09    0.000000E+00              9.00000E+100
24  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -2.944402E-08    0.000000E+00              9.00000E+100
25  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    5.821960E-09    0.000000E+00              9.00000E+100
26  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -2.788351E-09    0.000000E+00              9.00000E+100
27  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.861898E-09    0.000000E+00              9.00000E+100
28  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -2.061951E-09    0.000000E+00              9.00000E+100
29  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    4.536171E-10    0.000000E+00              9.00000E+100
30  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    6.582550E-09    0.000000E+00              9.00000E+100
31  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.989606E-09    0.000000E+00              9.00000E+100
32  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.409810E-09    0.000000E+00              9.00000E+100
33  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.032187E-11    0.000000E+00              9.00000E+100
34  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.340994E-09    0.000000E+00              9.00000E+100
35  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.680162E-10    0.000000E+00              9.00000E+100
36  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.996181E-10    0.000000E+00              9.00000E+100
37  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.754336E-10    0.000000E+00              9.00000E+100
38  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.325291E-09    0.000000E+00              9.00000E+100
39  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.187983E-09    0.000000E+00              9.00000E+100
40  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -1.362489E-12    0.000000E+00              9.00000E+100
41  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.803363E-10    0.000000E+00              9.00000E+100
42  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.203308E-10    0.000000E+00              9.00000E+100
43  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.395587E-10    0.000000E+00              9.00000E+100
44  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.006184E-10    0.000000E+00              9.00000E+100
45  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.067049E-10    0.000000E+00              9.00000E+100
46  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.689512E-10    0.000000E+00              9.00000E+100
47  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.436003E-10    0.000000E+00              9.00000E+100
48  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    1.986496E-11    0.000000E+00              9.00000E+100
49  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.064343E-09    0.000000E+00              9.00000E+100
50  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -4.928050E-11    0.000000E+00              9.00000E+100
51  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    2.049323E-12    0.000000E+00              9.00000E+100
52  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    9.780965E-10    0.000000E+00              9.00000E+100
53  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.048589E-09    0.000000E+00              9.00000E+100
54  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    4.401951E-10    0.000000E+00              9.00000E+100
55  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.153267E-10    0.000000E+00              9.00000E+100
56  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -4.020874E-10    0.000000E+00              9.00000E+100
57  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -3.189492E-10    0.000000E+00              9.00000E+100
58  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    6.674067E-11    0.000000E+00              9.00000E+100
59  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -2.629420E-13    0.000000E+00              9.00000E+100
60  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    1.154863E-10    0.000000E+00              9.00000E+100
61  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.887594E-10    0.000000E+00              9.00000E+100
62  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    4.729496E-11    0.000000E+00              9.00000E+100
63  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -1.150022E-12    0.000000E+00              9.00000E+100
64  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -6.633643E-12    0.000000E+00              9.00000E+100
65  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -4.255330E-12    0.000000E+00              9.00000E+100
66  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    8.835042E-13    0.000000E+00              9.00000E+100
67  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    3.071723E-11    0.000000E+00              9.00000E+100
68  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    1.247097E-10    0.000000E+00              9.00000E+100
69  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -9.313930E-12    0.000000E+00              9.00000E+100
70  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -2.782024E-12    0.000000E+00              9.00000E+100
71  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -2.103254E-12    0.000000E+00              9.00000E+100
72  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -6.311226E-14    0.000000E+00              9.00000E+100
73  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -8.996915E-13    0.000000E+00              9.00000E+100
74  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -1.867753E-12    0.000000E+00              9.00000E+100
75  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    1.376606E-12    0.000000E+00              9.00000E+100
76  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    1.089158E-11    0.000000E+00              9.00000E+100
77  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    3.165591E-13    0.000000E+00              9.00000E+100
78  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
79  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
80  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
81  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
82  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
83  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
84  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
85  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
86  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
87  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
88  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
89  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
90  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
91  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
92  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
93  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
94  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
95  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
96  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
97  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
98  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
99  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
100  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
101  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
102  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
103  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
104  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
105  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
106  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
107  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
108  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
109  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
110  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
111  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
112  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
113  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
114  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
115  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
116  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
117  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
118  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
119  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
120  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
121  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
122  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
123  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
124  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
125  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
126  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
127  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
128  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
129  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
130  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
131  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
132  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
133  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
134  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
135  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
136  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
137  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
138  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
139  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
140  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
141  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
142  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
143  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
144  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
145  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
146  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
147  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
148  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    1.918393E-12    0.000000E+00              9.00000E+100
149  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
150  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -4.513865E-13    0.000000E+00              9.00000E+100
151  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    2.256932E-13    0.000000E+00              9.00000E+100
152  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    1.354159E-12    0.000000E+00              9.00000E+100
153  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    4.513865E-13    0.000000E+00              9.00000E+100
154  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    1.015620E-12    0.000000E+00              9.00000E+100
155  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
156  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -6.665004E-13    0.000000E+00              9.00000E+100
157  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -1.001514E-12    0.000000E+00              9.00000E+100
158  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -8.745613E-13    0.000000E+00              9.00000E+100
159  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    2.256932E-13    0.000000E+00              9.00000E+100
160  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -6.770797E-13    0.000000E+00              9.00000E+100
161  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    4.513865E-13    0.000000E+00              9.00000E+100
162  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
163  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
164  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
165  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
166  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
167  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
168  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
169  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
170  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
171  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
172  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
173  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
174  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
175  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
176  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    5.000000E-03    1.000000E+00         l    9.00000E+100
177  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    5.000000E-03    1.000000E+00         l    9.00000E+100
178  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    1.223116E-02    1.000000E+00              9.00000E+100
179  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    1.223116E-02    1.000000E+00              9.00000E+100
180  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.913506E-02    1.000000E+00              9.00000E+100
181  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    1.261712E-01    1.000000E+00              9.00000E+100
182  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    1.261712E-01    1.000000E+00              9.00000E+100
183  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    2.186518E-01    1.000000E+00              9.00000E+100
184  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    2.989578E-01    1.000000E+00              9.00000E+100
185  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    2.989578E-01    1.000000E+00              9.00000E+100
186  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.667072E-01    1.000000E+00              9.00000E+100
187  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.234316E-01    1.000000E+00              9.00000E+100
188  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.234316E-01    1.000000E+00              9.00000E+100
189  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.525688E-01    1.000000E+00              9.00000E+100
190  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.419970E-01    1.000000E+00              9.00000E+100
191  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.419970E-01    1.000000E+00              9.00000E+100
192  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.029582E-01    1.000000E+00              9.00000E+100
193  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.667178E-01    1.000000E+00              9.00000E+100
194  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.667178E-01    1.000000E+00              9.00000E+100
195  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.529703E-01    1.000000E+00              9.00000E+100
196  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.573729E-01    1.000000E+00              9.00000E+100
197  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.573729E-01    1.000000E+00              9.00000E+100
198  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.707172E-01    1.000000E+00              9.00000E+100
199  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.857635E-01    1.000000E+00              9.00000E+100
200  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.857635E-01    1.000000E+00              9.00000E+100
201  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.995497E-01    1.000000E+00              9.00000E+100
202  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.131152E-01    1.000000E+00              9.00000E+100
203  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.131152E-01    1.000000E+00              9.00000E+100
204  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.272108E-01    1.000000E+00              9.00000E+100
205  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.407678E-01    1.000000E+00              9.00000E+100
206  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.407678E-01    1.000000E+00              9.00000E+100
207  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.513144E-01    1.000000E+00              9.00000E+100
208  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.569471E-01    1.000000E+00              9.00000E+100
209  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.569471E-01    1.000000E+00              9.00000E+100
210  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.579603E-01    1.000000E+00              9.00000E+100
211  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.681077E-01    1.000000E+00              9.00000E+100
212  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.681077E-01    1.000000E+00              9.00000E+100
213  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    5.120673E-01    1.000000E+00              9.00000E+100
214  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    6.037812E-01    1.000000E+00              9.00000E+100
215  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    6.037812E-01    1.000000E+00              9.00000E+100
216  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    7.330585E-01    1.000000E+00              9.00000E+100
217  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    8.631062E-01    1.000000E+00              9.00000E+100
218  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    8.631062E-01    1.000000E+00              9.00000E+100
219  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    9.610986E-01    1.000000E+00              9.00000E+100
220  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    4.000084E-01    1.800000E+00              9.00000E+100
221  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    5.901466E-01    1.800000E+00              9.00000E+100
222  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    7.761596E-01    1.800000E+00              9.00000E+100
223  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    7.761596E-01    1.800000E+00              9.00000E+100
224  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.011669E-01    1.800000E+00              9.00000E+100
225  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.395412E-01    1.800000E+00              9.00000E+100
226  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.395412E-01    1.800000E+00              9.00000E+100
227  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.347896E-01    1.800000E+00              9.00000E+100
228  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.317467E-01    1.800000E+00              9.00000E+100
229  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.317467E-01    1.800000E+00              9.00000E+100
230  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.276685E-01    1.800000E+00              9.00000E+100
231  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.287320E-01    1.800000E+00              9.00000E+100
232  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.287320E-01    1.800000E+00              9.00000E+100
233  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.732941E-01    1.800000E+00              9.00000E+100
234  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.066912E+00    1.800000E+00              9.00000E+100
235  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.066912E+00    1.800000E+00              9.00000E+100
236  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.177187E+00    1.800000E+00              9.00000E+100
237  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.267651E+00    1.800000E+00              9.00000E+100
238  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.267651E+00    1.800000E+00              9.00000E+100
239  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.324568E+00    1.800000E+00              9.00000E+100
240  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.361322E+00    1.800000E+00              9.00000E+100
241  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.361322E+00    1.800000E+00              9.00000E+100
242  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.391018E+00    1.800000E+00              9.00000E+100
243  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.420882E+00    1.800000E+00              9.00000E+100
244  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.420882E+00    1.800000E+00              9.00000E+100
245  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.453028E+00    1.800000E+00              9.00000E+100
246  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.486138E+00    1.800000E+00              9.00000E+100
247  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.486138E+00    1.800000E+00              9.00000E+100
248  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.519663E+00    1.800000E+00              9.00000E+100
249  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.555025E+00    1.800000E+00              9.00000E+100
250  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.555025E+00    1.800000E+00              9.00000E+100
251  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.594583E+00    1.800000E+00              9.00000E+100
252  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.638810E+00    1.800000E+00              9.00000E+100
253  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.638810E+00    1.800000E+00              9.00000E+100
254  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.685047E+00    1.800000E+00              9.00000E+100
255  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.718235E+00    1.800000E+00              9.00000E+100
256  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.718235E+00    1.800000E+00              9.00000E+100
257  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.716946E+00    1.800000E+00              9.00000E+100
258  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.635776E+00    1.800000E+00              9.00000E+100
259  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.635776E+00    1.800000E+00              9.00000E+100
260  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.459658E+00    1.800000E+00              9.00000E+100
261  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.256960E+00    1.800000E+00              9.00000E+100
262  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.256960E+00    1.800000E+00              9.00000E+100
263  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.081436E+00    1.800000E+00              9.00000E+100

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

/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/visualization/opt_report/opt_report.py:634: UserWarning: Attempting to set identical low and high ylims makes transformation singular; automatically expanding.
ax.set_ylim([ymin_plot, ymax_plot])

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

Done simulating trajectory traj

False

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

plot_results([('traj.phase0.timeseries.time', 'traj.phase0.timeseries.h',
'time (s)', 'altitude (m)'),
('traj.phase0.timeseries.time', 'traj.phase0.timeseries.alpha',
'time (s)', 'alpha (deg)')],
title='Supersonic Minimum Time-to-Climb Solution',
p_sol=sol, p_sim=sim)

plt.show()


## References#

[Bry99]

Arthur Earl Bryson. Dynamic optimization. Addison Wesley Longman Menlo Park, CA, 1999.