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.
Show 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
angle of attack (rad)
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)
self.add_subsystem(name='mach_comp',
subsys=MachComp(num_nodes=nn),
promotes_inputs=['v', 'sos'],
promotes_outputs=['mach'])
self.add_subsystem(name='cd0_comp',
subsys=CD0Comp(num_nodes=nn),
promotes_inputs=['mach'],
promotes_outputs=['CD0'])
self.add_subsystem(name='kappa_comp',
subsys=KappaComp(num_nodes=nn),
promotes_inputs=['mach'],
promotes_outputs=['kappa'])
self.add_subsystem(name='cla_comp',
subsys=CLaComp(num_nodes=nn),
promotes_inputs=['mach'],
promotes_outputs=['CLa'])
self.add_subsystem(name='CL_comp',
subsys=CLComp(num_nodes=nn),
promotes_inputs=['alpha', 'CLa'],
promotes_outputs=['CL'])
self.add_subsystem(name='CD_comp',
subsys=CDComp(num_nodes=nn),
promotes_inputs=['CD0', 'alpha', 'CLa', 'kappa'],
promotes_outputs=['CD'])
self.add_subsystem(name='q_comp',
subsys=q_comp,
promotes_inputs=['rho', 'v'],
promotes_outputs=['q'])
self.add_subsystem(name='lift_drag_force_comp',
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']
self.add_subsystem(name='atmos',
subsys=USatm1976Comp(num_nodes=nn, h_def='geodetic'),
promotes_inputs=['h'])
self.add_subsystem(name='aero',
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')
self.add_subsystem(name='prop',
subsys=PropGroup(num_nodes=nn),
promotes_inputs=['h', 'Isp', 'throttle'])
self.connect('aero.mach', 'prop.mach')
self.add_subsystem(name='flight_dynamics',
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))
traj.add_phase('phase0', phase)
p.model.add_subsystem('traj', traj)
#
# 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)
phase.add_state('r', fix_initial=True, lower=0, upper=1.0E6, units='m',
ref=1.0E3, defect_ref=1.0E3,
rate_source='flight_dynamics.r_dot')
phase.add_state('h', fix_initial=True, lower=0, upper=20000.0, units='m',
ref=1.0E2, defect_ref=1.0E2,
rate_source='flight_dynamics.h_dot')
phase.add_state('v', fix_initial=True, lower=10.0, units='m/s',
ref=1.0E2, defect_ref=1.0E2,
rate_source='flight_dynamics.v_dot')
phase.add_state('gam', fix_initial=True, lower=-1.5, upper=1.5, units='rad',
ref=1.0, defect_ref=1.0,
rate_source='flight_dynamics.gam_dot')
phase.add_state('m', fix_initial=True, lower=10.0, upper=1.0E5, units='kg',
ref=1.0E3, defect_ref=1.0E3,
rate_source='prop.m_dot')
phase.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0,
rate_continuity=True, rate_continuity_scaler=100.0,
rate2_continuity=False)
phase.add_parameter('S', val=49.2386, units='m**2', opt=False, targets=['S'])
phase.add_parameter('Isp', val=1600.0, units='s', opt=False, targets=['Isp'])
phase.add_parameter('throttle', val=1.0, opt=False, targets=['throttle'])
#
# Setup the boundary and path constraints
#
phase.add_boundary_constraint('h', loc='final', equals=20000, scaler=1.0E-3)
phase.add_boundary_constraint('aero.mach', loc='final', equals=1.0)
phase.add_boundary_constraint('gam', loc='final', equals=0.0)
phase.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000)
phase.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', ref=1.0)
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]
[final] 0.0000e+00 == gam [rad]
[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: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
INFO: checking unserializable_options
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
Model viewer data has already been recorded for Driver.
INFO: checking out_of_order
INFO: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
INFO: checking unserializable_options
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/driver.py:466: 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 for problem 'problem' was computed 3 times, taking 0.09052831799999694 seconds.
Total jacobian shape: (181, 191)
Jacobian shape: (181, 191) (5.28% nonzero)
FWD solves: 14 REV solves: 0
Total colors vs. total size: 14 vs 191 (92.67% improvement)
Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.0905 sec
Time to compute coloring: 0.1412 sec
Memory to compute coloring: 0.3750 MB
Coloring created on: 2024-03-29 20:24:28
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/total_jac.py:1627: DerivativesWarning:Constraints or objectives [('traj.phases.phase0->path_constraint->h', inds=[(0, 0)]), ('traj.phases.phase0->path_constraint->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: 5.3394
User Objective Time : 1.0883
User Sensitivity Time : 0.8632
Interface Time : 0.7027
Opt Solver Time: 2.6852
Calls to Objective Function : 125
Calls to Sens Function : 103
Objectives
Index Name Value
0 traj.phase0.t 3.252583E+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 3.252583E+00 4.000000E+00
1 traj.phase0.states:r_0 c 0.000000E+00 4.337706E+00 1.000000E+03
2 traj.phase0.states:r_1 c 0.000000E+00 4.337706E+00 1.000000E+03
3 traj.phase0.states:r_2 c 0.000000E+00 1.031184E+01 1.000000E+03
4 traj.phase0.states:r_3 c 0.000000E+00 1.031184E+01 1.000000E+03
5 traj.phase0.states:r_4 c 0.000000E+00 1.587221E+01 1.000000E+03
6 traj.phase0.states:r_5 c 0.000000E+00 1.587221E+01 1.000000E+03
7 traj.phase0.states:r_6 c 0.000000E+00 2.161221E+01 1.000000E+03
8 traj.phase0.states:r_7 c 0.000000E+00 2.161221E+01 1.000000E+03
9 traj.phase0.states:r_8 c 0.000000E+00 2.800703E+01 1.000000E+03
10 traj.phase0.states:r_9 c 0.000000E+00 2.800703E+01 1.000000E+03
11 traj.phase0.states:r_10 c 0.000000E+00 3.569230E+01 1.000000E+03
12 traj.phase0.states:r_11 c 0.000000E+00 3.569230E+01 1.000000E+03
13 traj.phase0.states:r_12 c 0.000000E+00 4.461248E+01 1.000000E+03
14 traj.phase0.states:r_13 c 0.000000E+00 4.461248E+01 1.000000E+03
15 traj.phase0.states:r_14 c 0.000000E+00 5.396205E+01 1.000000E+03
16 traj.phase0.states:r_15 c 0.000000E+00 5.396205E+01 1.000000E+03
17 traj.phase0.states:r_16 c 0.000000E+00 6.365729E+01 1.000000E+03
18 traj.phase0.states:r_17 c 0.000000E+00 6.365729E+01 1.000000E+03
19 traj.phase0.states:r_18 c 0.000000E+00 7.372225E+01 1.000000E+03
20 traj.phase0.states:r_19 c 0.000000E+00 7.372225E+01 1.000000E+03
21 traj.phase0.states:r_20 c 0.000000E+00 8.422625E+01 1.000000E+03
22 traj.phase0.states:r_21 c 0.000000E+00 8.422625E+01 1.000000E+03
23 traj.phase0.states:r_22 c 0.000000E+00 9.527842E+01 1.000000E+03
24 traj.phase0.states:r_23 c 0.000000E+00 9.527842E+01 1.000000E+03
25 traj.phase0.states:r_24 c 0.000000E+00 1.058989E+02 1.000000E+03
26 traj.phase0.states:r_25 c 0.000000E+00 1.058989E+02 1.000000E+03
27 traj.phase0.states:r_26 c 0.000000E+00 1.136098E+02 1.000000E+03
28 traj.phase0.states:r_27 c 0.000000E+00 1.136098E+02 1.000000E+03
29 traj.phase0.states:r_28 c 0.000000E+00 1.199409E+02 1.000000E+03
30 traj.phase0.states:h_0 c 0.000000E+00 2.446029E+00 2.000000E+02
31 traj.phase0.states:h_1 c 0.000000E+00 2.446029E+00 2.000000E+02
32 traj.phase0.states:h_2 c 0.000000E+00 2.523966E+01 2.000000E+02
33 traj.phase0.states:h_3 c 0.000000E+00 2.523966E+01 2.000000E+02
34 traj.phase0.states:h_4 c 0.000000E+00 5.979602E+01 2.000000E+02
35 traj.phase0.states:h_5 c 0.000000E+00 5.979602E+01 2.000000E+02
36 traj.phase0.states:h_6 c 0.000000E+00 8.469376E+01 2.000000E+02
37 traj.phase0.states:h_7 c 0.000000E+00 8.469376E+01 2.000000E+02
38 traj.phase0.states:h_8 c 0.000000E+00 8.840914E+01 2.000000E+02
39 traj.phase0.states:h_9 c 0.000000E+00 8.840914E+01 2.000000E+02
40 traj.phase0.states:h_10 c 0.000000E+00 7.334853E+01 2.000000E+02
41 traj.phase0.states:h_11 c 0.000000E+00 7.334853E+01 2.000000E+02
42 traj.phase0.states:h_12 c 0.000000E+00 7.147469E+01 2.000000E+02
43 traj.phase0.states:h_13 c 0.000000E+00 7.147469E+01 2.000000E+02
44 traj.phase0.states:h_14 c 0.000000E+00 7.714455E+01 2.000000E+02
45 traj.phase0.states:h_15 c 0.000000E+00 7.714455E+01 2.000000E+02
46 traj.phase0.states:h_16 c 0.000000E+00 8.258633E+01 2.000000E+02
47 traj.phase0.states:h_17 c 0.000000E+00 8.258633E+01 2.000000E+02
48 traj.phase0.states:h_18 c 0.000000E+00 8.812291E+01 2.000000E+02
49 traj.phase0.states:h_19 c 0.000000E+00 8.812291E+01 2.000000E+02
50 traj.phase0.states:h_20 c 0.000000E+00 9.138648E+01 2.000000E+02
51 traj.phase0.states:h_21 c 0.000000E+00 9.138648E+01 2.000000E+02
52 traj.phase0.states:h_22 c 0.000000E+00 9.361784E+01 2.000000E+02
53 traj.phase0.states:h_23 c 0.000000E+00 9.361784E+01 2.000000E+02
54 traj.phase0.states:h_24 c 0.000000E+00 1.207569E+02 2.000000E+02
55 traj.phase0.states:h_25 c 0.000000E+00 1.207569E+02 2.000000E+02
56 traj.phase0.states:h_26 c 0.000000E+00 1.726189E+02 2.000000E+02
57 traj.phase0.states:h_27 c 0.000000E+00 1.726189E+02 2.000000E+02
58 traj.phase0.states:h_28 c 0.000000E+00 2.000000E+02 2.000000E+02 u
59 traj.phase0.states:v_0 c 1.000000E-01 2.633882E+00 1.000000E+19
60 traj.phase0.states:v_1 c 1.000000E-01 2.633882E+00 1.000000E+19
61 traj.phase0.states:v_2 c 1.000000E-01 3.104671E+00 1.000000E+19
62 traj.phase0.states:v_3 c 1.000000E-01 3.104671E+00 1.000000E+19
63 traj.phase0.states:v_4 c 1.000000E-01 2.949158E+00 1.000000E+19
64 traj.phase0.states:v_5 c 1.000000E-01 2.949158E+00 1.000000E+19
65 traj.phase0.states:v_6 c 1.000000E-01 2.842674E+00 1.000000E+19
66 traj.phase0.states:v_7 c 1.000000E-01 2.842674E+00 1.000000E+19
67 traj.phase0.states:v_8 c 1.000000E-01 3.248801E+00 1.000000E+19
68 traj.phase0.states:v_9 c 1.000000E-01 3.248801E+00 1.000000E+19
69 traj.phase0.states:v_10 c 1.000000E-01 3.941025E+00 1.000000E+19
70 traj.phase0.states:v_11 c 1.000000E-01 3.941025E+00 1.000000E+19
71 traj.phase0.states:v_12 c 1.000000E-01 4.243043E+00 1.000000E+19
72 traj.phase0.states:v_13 c 1.000000E-01 4.243043E+00 1.000000E+19
73 traj.phase0.states:v_14 c 1.000000E-01 4.395001E+00 1.000000E+19
74 traj.phase0.states:v_15 c 1.000000E-01 4.395001E+00 1.000000E+19
75 traj.phase0.states:v_16 c 1.000000E-01 4.563111E+00 1.000000E+19
76 traj.phase0.states:v_17 c 1.000000E-01 4.563111E+00 1.000000E+19
77 traj.phase0.states:v_18 c 1.000000E-01 4.737651E+00 1.000000E+19
78 traj.phase0.states:v_19 c 1.000000E-01 4.737651E+00 1.000000E+19
79 traj.phase0.states:v_20 c 1.000000E-01 4.969663E+00 1.000000E+19
80 traj.phase0.states:v_21 c 1.000000E-01 4.969663E+00 1.000000E+19
81 traj.phase0.states:v_22 c 1.000000E-01 5.194006E+00 1.000000E+19
82 traj.phase0.states:v_23 c 1.000000E-01 5.194006E+00 1.000000E+19
83 traj.phase0.states:v_24 c 1.000000E-01 4.826572E+00 1.000000E+19
84 traj.phase0.states:v_25 c 1.000000E-01 4.826572E+00 1.000000E+19
85 traj.phase0.states:v_26 c 1.000000E-01 3.708917E+00 1.000000E+19
86 traj.phase0.states:v_27 c 1.000000E-01 3.708917E+00 1.000000E+19
87 traj.phase0.states:v_28 c 1.000000E-01 2.950719E+00 1.000000E+19
88 traj.phase0.states:gam_0 c -1.500000E+00 1.014493E-01 1.500000E+00
89 traj.phase0.states:gam_1 c -1.500000E+00 1.014493E-01 1.500000E+00
90 traj.phase0.states:gam_2 c -1.500000E+00 5.979443E-01 1.500000E+00
91 traj.phase0.states:gam_3 c -1.500000E+00 5.979443E-01 1.500000E+00
92 traj.phase0.states:gam_4 c -1.500000E+00 4.557325E-01 1.500000E+00
93 traj.phase0.states:gam_5 c -1.500000E+00 4.557325E-01 1.500000E+00
94 traj.phase0.states:gam_6 c -1.500000E+00 3.191609E-01 1.500000E+00
95 traj.phase0.states:gam_7 c -1.500000E+00 3.191609E-01 1.500000E+00
96 traj.phase0.states:gam_8 c -1.500000E+00 -1.775656E-01 1.500000E+00
97 traj.phase0.states:gam_9 c -1.500000E+00 -1.775656E-01 1.500000E+00
98 traj.phase0.states:gam_10 c -1.500000E+00 -1.196090E-01 1.500000E+00
99 traj.phase0.states:gam_11 c -1.500000E+00 -1.196090E-01 1.500000E+00
100 traj.phase0.states:gam_12 c -1.500000E+00 4.688152E-02 1.500000E+00
101 traj.phase0.states:gam_13 c -1.500000E+00 4.688152E-02 1.500000E+00
102 traj.phase0.states:gam_14 c -1.500000E+00 5.957514E-02 1.500000E+00
103 traj.phase0.states:gam_15 c -1.500000E+00 5.957514E-02 1.500000E+00
104 traj.phase0.states:gam_16 c -1.500000E+00 5.533961E-02 1.500000E+00
105 traj.phase0.states:gam_17 c -1.500000E+00 5.533961E-02 1.500000E+00
106 traj.phase0.states:gam_18 c -1.500000E+00 4.987172E-02 1.500000E+00
107 traj.phase0.states:gam_19 c -1.500000E+00 4.987172E-02 1.500000E+00
108 traj.phase0.states:gam_20 c -1.500000E+00 1.063274E-02 1.500000E+00
109 traj.phase0.states:gam_21 c -1.500000E+00 1.063274E-02 1.500000E+00
110 traj.phase0.states:gam_22 c -1.500000E+00 7.519137E-02 1.500000E+00
111 traj.phase0.states:gam_23 c -1.500000E+00 7.519137E-02 1.500000E+00
112 traj.phase0.states:gam_24 c -1.500000E+00 4.620378E-01 1.500000E+00
113 traj.phase0.states:gam_25 c -1.500000E+00 4.620378E-01 1.500000E+00
114 traj.phase0.states:gam_26 c -1.500000E+00 6.283286E-01 1.500000E+00
115 traj.phase0.states:gam_27 c -1.500000E+00 6.283286E-01 1.500000E+00
116 traj.phase0.states:gam_28 c -1.500000E+00 0.000000E+00 1.500000E+00
117 traj.phase0.states:m_0 c 1.000000E-02 1.883945E+01 1.000000E+02
118 traj.phase0.states:m_1 c 1.000000E-02 1.883945E+01 1.000000E+02
119 traj.phase0.states:m_2 c 1.000000E-02 1.863480E+01 1.000000E+02
120 traj.phase0.states:m_3 c 1.000000E-02 1.863480E+01 1.000000E+02
121 traj.phase0.states:m_4 c 1.000000E-02 1.847308E+01 1.000000E+02
122 traj.phase0.states:m_5 c 1.000000E-02 1.847308E+01 1.000000E+02
123 traj.phase0.states:m_6 c 1.000000E-02 1.835400E+01 1.000000E+02
124 traj.phase0.states:m_7 c 1.000000E-02 1.835400E+01 1.000000E+02
125 traj.phase0.states:m_8 c 1.000000E-02 1.825101E+01 1.000000E+02
126 traj.phase0.states:m_9 c 1.000000E-02 1.825101E+01 1.000000E+02
127 traj.phase0.states:m_10 c 1.000000E-02 1.811459E+01 1.000000E+02
128 traj.phase0.states:m_11 c 1.000000E-02 1.811459E+01 1.000000E+02
129 traj.phase0.states:m_12 c 1.000000E-02 1.794316E+01 1.000000E+02
130 traj.phase0.states:m_13 c 1.000000E-02 1.794316E+01 1.000000E+02
131 traj.phase0.states:m_14 c 1.000000E-02 1.776707E+01 1.000000E+02
132 traj.phase0.states:m_15 c 1.000000E-02 1.776707E+01 1.000000E+02
133 traj.phase0.states:m_16 c 1.000000E-02 1.759239E+01 1.000000E+02
134 traj.phase0.states:m_17 c 1.000000E-02 1.759239E+01 1.000000E+02
135 traj.phase0.states:m_18 c 1.000000E-02 1.741882E+01 1.000000E+02
136 traj.phase0.states:m_19 c 1.000000E-02 1.741882E+01 1.000000E+02
137 traj.phase0.states:m_20 c 1.000000E-02 1.724476E+01 1.000000E+02
138 traj.phase0.states:m_21 c 1.000000E-02 1.724476E+01 1.000000E+02
139 traj.phase0.states:m_22 c 1.000000E-02 1.706462E+01 1.000000E+02
140 traj.phase0.states:m_23 c 1.000000E-02 1.706462E+01 1.000000E+02
141 traj.phase0.states:m_24 c 1.000000E-02 1.690433E+01 1.000000E+02
142 traj.phase0.states:m_25 c 1.000000E-02 1.690433E+01 1.000000E+02
143 traj.phase0.states:m_26 c 1.000000E-02 1.682842E+01 1.000000E+02
144 traj.phase0.states:m_27 c 1.000000E-02 1.682842E+01 1.000000E+02
145 traj.phase0.states:m_28 c 1.000000E-02 1.680487E+01 1.000000E+02
146 traj.phase0.controls:alpha_0 c -8.000000E+00 5.400658E+00 8.000000E+00
147 traj.phase0.controls:alpha_1 c -8.000000E+00 2.645922E+00 8.000000E+00
148 traj.phase0.controls:alpha_2 c -8.000000E+00 2.027262E+00 8.000000E+00
149 traj.phase0.controls:alpha_3 c -8.000000E+00 2.027262E+00 8.000000E+00
150 traj.phase0.controls:alpha_4 c -8.000000E+00 2.080183E+00 8.000000E+00
151 traj.phase0.controls:alpha_5 c -8.000000E+00 1.340193E+00 8.000000E+00
152 traj.phase0.controls:alpha_6 c -8.000000E+00 1.340193E+00 8.000000E+00
153 traj.phase0.controls:alpha_7 c -8.000000E+00 7.773049E-01 8.000000E+00
154 traj.phase0.controls:alpha_8 c -8.000000E+00 1.361534E+00 8.000000E+00
155 traj.phase0.controls:alpha_9 c -8.000000E+00 1.361534E+00 8.000000E+00
156 traj.phase0.controls:alpha_10 c -8.000000E+00 1.892584E+00 8.000000E+00
157 traj.phase0.controls:alpha_11 c -8.000000E+00 1.170161E+00 8.000000E+00
158 traj.phase0.controls:alpha_12 c -8.000000E+00 1.170161E+00 8.000000E+00
159 traj.phase0.controls:alpha_13 c -8.000000E+00 4.830056E-01 8.000000E+00
160 traj.phase0.controls:alpha_14 c -8.000000E+00 1.119857E+00 8.000000E+00
161 traj.phase0.controls:alpha_15 c -8.000000E+00 1.119857E+00 8.000000E+00
162 traj.phase0.controls:alpha_16 c -8.000000E+00 1.997080E+00 8.000000E+00
163 traj.phase0.controls:alpha_17 c -8.000000E+00 2.031038E+00 8.000000E+00
164 traj.phase0.controls:alpha_18 c -8.000000E+00 2.031038E+00 8.000000E+00
165 traj.phase0.controls:alpha_19 c -8.000000E+00 1.681271E+00 8.000000E+00
166 traj.phase0.controls:alpha_20 c -8.000000E+00 1.407316E+00 8.000000E+00
167 traj.phase0.controls:alpha_21 c -8.000000E+00 1.407316E+00 8.000000E+00
168 traj.phase0.controls:alpha_22 c -8.000000E+00 1.239354E+00 8.000000E+00
169 traj.phase0.controls:alpha_23 c -8.000000E+00 1.207563E+00 8.000000E+00
170 traj.phase0.controls:alpha_24 c -8.000000E+00 1.207563E+00 8.000000E+00
171 traj.phase0.controls:alpha_25 c -8.000000E+00 1.240086E+00 8.000000E+00
172 traj.phase0.controls:alpha_26 c -8.000000E+00 1.265067E+00 8.000000E+00
173 traj.phase0.controls:alpha_27 c -8.000000E+00 1.265067E+00 8.000000E+00
174 traj.phase0.controls:alpha_28 c -8.000000E+00 1.260861E+00 8.000000E+00
175 traj.phase0.controls:alpha_29 c -8.000000E+00 1.205823E+00 8.000000E+00
176 traj.phase0.controls:alpha_30 c -8.000000E+00 1.205823E+00 8.000000E+00
177 traj.phase0.controls:alpha_31 c -8.000000E+00 1.150393E+00 8.000000E+00
178 traj.phase0.controls:alpha_32 c -8.000000E+00 1.145010E+00 8.000000E+00
179 traj.phase0.controls:alpha_33 c -8.000000E+00 1.145010E+00 8.000000E+00
180 traj.phase0.controls:alpha_34 c -8.000000E+00 1.350321E+00 8.000000E+00
181 traj.phase0.controls:alpha_35 c -8.000000E+00 1.926970E+00 8.000000E+00
182 traj.phase0.controls:alpha_36 c -8.000000E+00 1.926970E+00 8.000000E+00
183 traj.phase0.controls:alpha_37 c -8.000000E+00 2.729913E+00 8.000000E+00
184 traj.phase0.controls:alpha_38 c -8.000000E+00 3.614100E+00 8.000000E+00
185 traj.phase0.controls:alpha_39 c -8.000000E+00 3.614100E+00 8.000000E+00
186 traj.phase0.controls:alpha_40 c -8.000000E+00 3.938262E+00 8.000000E+00
187 traj.phase0.controls:alpha_41 c -8.000000E+00 3.061127E+00 8.000000E+00
188 traj.phase0.controls:alpha_42 c -8.000000E+00 3.061127E+00 8.000000E+00
189 traj.phase0.controls:alpha_43 c -8.000000E+00 -9.747931E-02 8.000000E+00
190 traj.phase0.controls:alpha_44 c -8.000000E+00 -6.617732E+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.phase0.collocation_constraint.defects:r e 0.000000E+00 9.626221E-11 0.000000E+00 9.00000E+100
4 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.368485E-10 0.000000E+00 9.00000E+100
5 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.190306E-11 0.000000E+00 9.00000E+100
6 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 7.029587E-10 0.000000E+00 9.00000E+100
7 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.832643E-09 0.000000E+00 9.00000E+100
8 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.682121E-10 0.000000E+00 9.00000E+100
9 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.226231E-09 0.000000E+00 9.00000E+100
10 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 7.052637E-09 0.000000E+00 9.00000E+100
11 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.649110E-09 0.000000E+00 9.00000E+100
12 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.387493E-08 0.000000E+00 9.00000E+100
13 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.312753E-09 0.000000E+00 9.00000E+100
14 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.635311E-09 0.000000E+00 9.00000E+100
15 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.094938E-08 0.000000E+00 9.00000E+100
16 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.446385E-09 0.000000E+00 9.00000E+100
17 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.249223E-09 0.000000E+00 9.00000E+100
18 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 5.610081E-10 0.000000E+00 9.00000E+100
19 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 7.633869E-11 0.000000E+00 9.00000E+100
20 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.025378E-08 0.000000E+00 9.00000E+100
21 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 4.863413E-09 0.000000E+00 9.00000E+100
22 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 8.137628E-09 0.000000E+00 9.00000E+100
23 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 7.240734E-09 0.000000E+00 9.00000E+100
24 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -7.944413E-09 0.000000E+00 9.00000E+100
25 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.765342E-08 0.000000E+00 9.00000E+100
26 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 6.359086E-08 0.000000E+00 9.00000E+100
27 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -3.293199E-08 0.000000E+00 9.00000E+100
28 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -7.797211E-09 0.000000E+00 9.00000E+100
29 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.576675E-08 0.000000E+00 9.00000E+100
30 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 9.957874E-08 0.000000E+00 9.00000E+100
31 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 6.840250E-09 0.000000E+00 9.00000E+100
32 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -2.149195E-08 0.000000E+00 9.00000E+100
33 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.938033E-11 0.000000E+00 9.00000E+100
34 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 4.970212E-10 0.000000E+00 9.00000E+100
35 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 3.110582E-10 0.000000E+00 9.00000E+100
36 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.049736E-09 0.000000E+00 9.00000E+100
37 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 5.407972E-13 0.000000E+00 9.00000E+100
38 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 3.931003E-10 0.000000E+00 9.00000E+100
39 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 5.179055E-10 0.000000E+00 9.00000E+100
40 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.776728E-09 0.000000E+00 9.00000E+100
41 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 4.975365E-09 0.000000E+00 9.00000E+100
42 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.467697E-09 0.000000E+00 9.00000E+100
43 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.765677E-09 0.000000E+00 9.00000E+100
44 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 8.495683E-10 0.000000E+00 9.00000E+100
45 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.938764E-10 0.000000E+00 9.00000E+100
46 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 3.655915E-09 0.000000E+00 9.00000E+100
47 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.912653E-09 0.000000E+00 9.00000E+100
48 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 6.511562E-12 0.000000E+00 9.00000E+100
49 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -4.033623E-10 0.000000E+00 9.00000E+100
50 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 1.268023E-10 0.000000E+00 9.00000E+100
51 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -2.257089E-09 0.000000E+00 9.00000E+100
52 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -5.075319E-10 0.000000E+00 9.00000E+100
53 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -4.854685E-10 0.000000E+00 9.00000E+100
54 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -6.164998E-10 0.000000E+00 9.00000E+100
55 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -7.899700E-10 0.000000E+00 9.00000E+100
56 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -4.984145E-09 0.000000E+00 9.00000E+100
57 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -1.044732E-09 0.000000E+00 9.00000E+100
58 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -1.340575E-09 0.000000E+00 9.00000E+100
59 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -8.149447E-10 0.000000E+00 9.00000E+100
60 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -6.668500E-10 0.000000E+00 9.00000E+100
61 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -3.941808E-09 0.000000E+00 9.00000E+100
62 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -4.597335E-10 0.000000E+00 9.00000E+100
63 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -7.289592E-13 0.000000E+00 9.00000E+100
64 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -2.702542E-12 0.000000E+00 9.00000E+100
65 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 2.396880E-12 0.000000E+00 9.00000E+100
66 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 1.576115E-11 0.000000E+00 9.00000E+100
67 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 3.564389E-12 0.000000E+00 9.00000E+100
68 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 4.464979E-11 0.000000E+00 9.00000E+100
69 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -1.963587E-12 0.000000E+00 9.00000E+100
70 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -1.278074E-11 0.000000E+00 9.00000E+100
71 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -1.030847E-12 0.000000E+00 9.00000E+100
72 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -2.965951E-11 0.000000E+00 9.00000E+100
73 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -1.112910E-11 0.000000E+00 9.00000E+100
74 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 1.631636E-13 0.000000E+00 9.00000E+100
75 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 5.195264E-12 0.000000E+00 9.00000E+100
76 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 2.246188E-10 0.000000E+00 9.00000E+100
77 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 2.561390E-11 0.000000E+00 9.00000E+100
78 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
79 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
80 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
81 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
82 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
83 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
84 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
85 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
86 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
87 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
88 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
89 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
90 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
91 traj.phase0.continuity_comp.defect_states:r e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
92 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
93 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
94 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
95 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
96 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
97 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
98 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
99 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
100 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
101 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
102 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
103 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
104 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
105 traj.phase0.continuity_comp.defect_states:h e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
106 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
107 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
108 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
109 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
110 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
111 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
112 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
113 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
114 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
115 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
116 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
117 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
118 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
119 traj.phase0.continuity_comp.defect_states:v e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
120 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
121 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
122 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
123 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
124 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
125 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
126 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
127 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
128 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
129 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
130 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
131 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
132 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
133 traj.phase0.continuity_comp.defect_states:gam e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
134 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
135 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
136 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
137 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
138 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
139 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
140 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
141 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
142 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
143 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
144 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
145 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
146 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
147 traj.phase0.continuity_comp.defect_states:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
148 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 6.770799E-13 0.000000E+00 9.00000E+100
149 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 4.513866E-13 0.000000E+00 9.00000E+100
150 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
151 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
152 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 1.128466E-12 0.000000E+00 9.00000E+100
153 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 2.256933E-13 0.000000E+00 9.00000E+100
154 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 -3.385399E-13 0.000000E+00 9.00000E+100
155 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 -3.314870E-13 0.000000E+00 9.00000E+100
156 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 1.692700E-13 0.000000E+00 9.00000E+100
157 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 -6.770799E-13 0.000000E+00 9.00000E+100
158 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 2.856431E-13 0.000000E+00 9.00000E+100
159 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 -4.513866E-13 0.000000E+00 9.00000E+100
160 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 2.256933E-12 0.000000E+00 9.00000E+100
161 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 -1.354160E-12 0.000000E+00 9.00000E+100
162 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
163 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
164 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
165 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
166 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
167 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
168 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
169 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
170 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
171 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
172 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
173 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
174 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
175 traj.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 1.223015E-02 1.000000E+00 9.00000E+100
179 traj.phases.phase0->path_constraint->h i 5.000000E-03 1.223015E-02 1.000000E+00 9.00000E+100
180 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.914293E-02 1.000000E+00 9.00000E+100
181 traj.phases.phase0->path_constraint->h i 5.000000E-03 1.261983E-01 1.000000E+00 9.00000E+100
182 traj.phases.phase0->path_constraint->h i 5.000000E-03 1.261983E-01 1.000000E+00 9.00000E+100
183 traj.phases.phase0->path_constraint->h i 5.000000E-03 2.186847E-01 1.000000E+00 9.00000E+100
184 traj.phases.phase0->path_constraint->h i 5.000000E-03 2.989801E-01 1.000000E+00 9.00000E+100
185 traj.phases.phase0->path_constraint->h i 5.000000E-03 2.989801E-01 1.000000E+00 9.00000E+100
186 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.667273E-01 1.000000E+00 9.00000E+100
187 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.234688E-01 1.000000E+00 9.00000E+100
188 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.234688E-01 1.000000E+00 9.00000E+100
189 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.526223E-01 1.000000E+00 9.00000E+100
190 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.420457E-01 1.000000E+00 9.00000E+100
191 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.420457E-01 1.000000E+00 9.00000E+100
192 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.029903E-01 1.000000E+00 9.00000E+100
193 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.667426E-01 1.000000E+00 9.00000E+100
194 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.667426E-01 1.000000E+00 9.00000E+100
195 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.529900E-01 1.000000E+00 9.00000E+100
196 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.573735E-01 1.000000E+00 9.00000E+100
197 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.573735E-01 1.000000E+00 9.00000E+100
198 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.706966E-01 1.000000E+00 9.00000E+100
199 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.857227E-01 1.000000E+00 9.00000E+100
200 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.857227E-01 1.000000E+00 9.00000E+100
201 traj.phases.phase0->path_constraint->h i 5.000000E-03 3.994530E-01 1.000000E+00 9.00000E+100
202 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.129316E-01 1.000000E+00 9.00000E+100
203 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.129316E-01 1.000000E+00 9.00000E+100
204 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.269929E-01 1.000000E+00 9.00000E+100
205 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.406146E-01 1.000000E+00 9.00000E+100
206 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.406146E-01 1.000000E+00 9.00000E+100
207 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.512581E-01 1.000000E+00 9.00000E+100
208 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.569324E-01 1.000000E+00 9.00000E+100
209 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.569324E-01 1.000000E+00 9.00000E+100
210 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.579391E-01 1.000000E+00 9.00000E+100
211 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.680892E-01 1.000000E+00 9.00000E+100
212 traj.phases.phase0->path_constraint->h i 5.000000E-03 4.680892E-01 1.000000E+00 9.00000E+100
213 traj.phases.phase0->path_constraint->h i 5.000000E-03 5.120660E-01 1.000000E+00 9.00000E+100
214 traj.phases.phase0->path_constraint->h i 5.000000E-03 6.037847E-01 1.000000E+00 9.00000E+100
215 traj.phases.phase0->path_constraint->h i 5.000000E-03 6.037847E-01 1.000000E+00 9.00000E+100
216 traj.phases.phase0->path_constraint->h i 5.000000E-03 7.330530E-01 1.000000E+00 9.00000E+100
217 traj.phases.phase0->path_constraint->h i 5.000000E-03 8.630944E-01 1.000000E+00 9.00000E+100
218 traj.phases.phase0->path_constraint->h i 5.000000E-03 8.630944E-01 1.000000E+00 9.00000E+100
219 traj.phases.phase0->path_constraint->h i 5.000000E-03 9.610925E-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 5.901464E-01 1.800000E+00 9.00000E+100
222 traj.phases.phase0->path_constraint->mach i 1.000000E-01 7.761622E-01 1.800000E+00 9.00000E+100
223 traj.phases.phase0->path_constraint->mach i 1.000000E-01 7.761622E-01 1.800000E+00 9.00000E+100
224 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.011492E-01 1.800000E+00 9.00000E+100
225 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.394945E-01 1.800000E+00 9.00000E+100
226 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.394945E-01 1.800000E+00 9.00000E+100
227 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.347430E-01 1.800000E+00 9.00000E+100
228 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.317176E-01 1.800000E+00 9.00000E+100
229 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.317176E-01 1.800000E+00 9.00000E+100
230 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.276321E-01 1.800000E+00 9.00000E+100
231 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.286508E-01 1.800000E+00 9.00000E+100
232 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.286508E-01 1.800000E+00 9.00000E+100
233 traj.phases.phase0->path_constraint->mach i 1.000000E-01 9.731987E-01 1.800000E+00 9.00000E+100
234 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.066851E+00 1.800000E+00 9.00000E+100
235 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.066851E+00 1.800000E+00 9.00000E+100
236 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.177153E+00 1.800000E+00 9.00000E+100
237 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.267623E+00 1.800000E+00 9.00000E+100
238 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.267623E+00 1.800000E+00 9.00000E+100
239 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.324551E+00 1.800000E+00 9.00000E+100
240 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.361332E+00 1.800000E+00 9.00000E+100
241 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.361332E+00 1.800000E+00 9.00000E+100
242 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.391048E+00 1.800000E+00 9.00000E+100
243 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.420933E+00 1.800000E+00 9.00000E+100
244 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.420933E+00 1.800000E+00 9.00000E+100
245 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.453146E+00 1.800000E+00 9.00000E+100
246 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.486339E+00 1.800000E+00 9.00000E+100
247 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.486339E+00 1.800000E+00 9.00000E+100
248 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.519865E+00 1.800000E+00 9.00000E+100
249 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.555138E+00 1.800000E+00 9.00000E+100
250 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.555138E+00 1.800000E+00 9.00000E+100
251 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.594613E+00 1.800000E+00 9.00000E+100
252 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.638818E+00 1.800000E+00 9.00000E+100
253 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.638818E+00 1.800000E+00 9.00000E+100
254 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.685059E+00 1.800000E+00 9.00000E+100
255 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.718237E+00 1.800000E+00 9.00000E+100
256 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.718237E+00 1.800000E+00 9.00000E+100
257 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.716938E+00 1.800000E+00 9.00000E+100
258 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.635775E+00 1.800000E+00 9.00000E+100
259 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.635775E+00 1.800000E+00 9.00000E+100
260 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.459678E+00 1.800000E+00 9.00000E+100
261 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.256990E+00 1.800000E+00 9.00000E+100
262 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.256990E+00 1.800000E+00 9.00000E+100
263 traj.phases.phase0->path_constraint->mach i 1.000000E-01 1.081459E+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: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/python3.10/site-packages/openmdao/core/group.py:1098: DerivativesWarning:Constraints or objectives [ode_eval.control_interp.control_rates:alpha_rate2] cannot be impacted by the design variables of the problem because no partials were defined for them in their parent component(s).
Simulating trajectory traj
Model viewer data has already been recorded for Driver.
Done simulating trajectory traj
False
sol = om.CaseReader('dymos_solution.db').get_case('final')
sim = om.CaseReader('dymos_simulation.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.