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Supersonic Interceptor Minimum Time Climb

This example is based on the A/C Min Time to Climb example given in chapter 4 of Bryson1. 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 free-body-diagram of the min-time-climb problem.

The vehicle dynamics are given by

\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

\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

\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.

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import openmdao.api as om
from ...models.atmosphere import USatm1976Comp
from .aero import AeroGroup
from .prop import PropGroup
from ...models.eom import FlightPathEOM2D


class MinTimeClimbODE(om.Group):

    def initialize(self):
        self.options.declare('num_nodes', types=int)

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

        self.add_subsystem(name='atmos',
                           subsys=USatm1976Comp(num_nodes=nn),
                           promotes_inputs=['h'])

        self.add_subsystem(name='aero',
                           subsys=AeroGroup(num_nodes=nn),
                           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
from openmdao.utils.assert_utils import assert_near_equal

import dymos as dm
from dymos.examples.min_time_climb.min_time_climb_ode import MinTimeClimbODE
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['traj.phase0.states:r'] = phase.interpolate(ys=[0.0, 50000.0], nodes='state_input')
p['traj.phase0.states:h'] = phase.interpolate(ys=[100.0, 20000.0], nodes='state_input')
p['traj.phase0.states:v'] = phase.interpolate(ys=[135.964, 283.159], nodes='state_input')
p['traj.phase0.states:gam'] = phase.interpolate(ys=[0.0, 0.0], nodes='state_input')
p['traj.phase0.states:m'] = phase.interpolate(ys=[19030.468, 10000.], nodes='state_input')
p['traj.phase0.controls:alpha'] = phase.interpolate(ys=[0.0, 0.0], nodes='control_input')

#
# Solve for the optimal trajectory
#
dm.run_problem(p)

#
# Test the results
#


#
# Get the explicitly simulated solution and plot the results
#
exp_out = traj.simulate()

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

plt.show()
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 comp_has_no_outputs
INFO: checking auto_ivc_warnings
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 comp_has_no_outputs
INFO: checking auto_ivc_warnings
Full total jacobian was computed 3 times, taking 0.333669 seconds.
Total jacobian shape: (181, 191) 


Jacobian shape: (181, 191)  ( 5.50% nonzero)
FWD solves: 13   REV solves: 0
Total colors vs. total size: 13 vs 191  (93.2% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.333669 sec.
Time to compute coloring: 0.008426 sec.


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

    Solution: 
--------------------------------------------------------------------------------
    Total Time:                   11.7976
       User Objective Time :       2.5130
       User Sensitivity Time :     2.3000
       Interface Time :            2.7305
       Opt Solver Time:            4.2541
    Calls to Objective Function :     154
    Calls to Sens Function :          128


   Objectives
      Index  Name                                    Value          Optimum
          0  traj.phases.phase0.time.time     3.240596E+02     0.000000E+00

   Variables (c - continuous, i - integer, d - discrete)
      Index  Name                                                                Type      Lower Bound            Value      Upper Bound     Status
          0  traj.phases.phase0.time_extents.t_duration_0                           c     5.000000E-01     3.240596E+00     4.000000E+00           
          1  traj.phases.phase0.indep_states.states:r_0                             c     0.000000E+00     4.317508E+00     1.000000E+03           
          2  traj.phases.phase0.indep_states.states:r_1                             c     0.000000E+00     4.317508E+00     1.000000E+03           
          3  traj.phases.phase0.indep_states.states:r_2                             c     0.000000E+00     1.027157E+01     1.000000E+03           
          4  traj.phases.phase0.indep_states.states:r_3                             c     0.000000E+00     1.027157E+01     1.000000E+03           
          5  traj.phases.phase0.indep_states.states:r_4                             c     0.000000E+00     1.580742E+01     1.000000E+03           
          6  traj.phases.phase0.indep_states.states:r_5                             c     0.000000E+00     1.580742E+01     1.000000E+03           
          7  traj.phases.phase0.indep_states.states:r_6                             c     0.000000E+00     2.152488E+01     1.000000E+03           
          8  traj.phases.phase0.indep_states.states:r_7                             c     0.000000E+00     2.152488E+01     1.000000E+03           
          9  traj.phases.phase0.indep_states.states:r_8                             c     0.000000E+00     2.789625E+01     1.000000E+03           
         10  traj.phases.phase0.indep_states.states:r_9                             c     0.000000E+00     2.789625E+01     1.000000E+03           
         11  traj.phases.phase0.indep_states.states:r_10                            c     0.000000E+00     3.554657E+01     1.000000E+03           
         12  traj.phases.phase0.indep_states.states:r_11                            c     0.000000E+00     3.554657E+01     1.000000E+03           
         13  traj.phases.phase0.indep_states.states:r_12                            c     0.000000E+00     4.442392E+01     1.000000E+03           
         14  traj.phases.phase0.indep_states.states:r_13                            c     0.000000E+00     4.442392E+01     1.000000E+03           
         15  traj.phases.phase0.indep_states.states:r_14                            c     0.000000E+00     5.373121E+01     1.000000E+03           
         16  traj.phases.phase0.indep_states.states:r_15                            c     0.000000E+00     5.373121E+01     1.000000E+03           
         17  traj.phases.phase0.indep_states.states:r_16                            c     0.000000E+00     6.338208E+01     1.000000E+03           
         18  traj.phases.phase0.indep_states.states:r_17                            c     0.000000E+00     6.338208E+01     1.000000E+03           
         19  traj.phases.phase0.indep_states.states:r_18                            c     0.000000E+00     7.340193E+01     1.000000E+03           
         20  traj.phases.phase0.indep_states.states:r_19                            c     0.000000E+00     7.340193E+01     1.000000E+03           
         21  traj.phases.phase0.indep_states.states:r_20                            c     0.000000E+00     8.386398E+01     1.000000E+03           
         22  traj.phases.phase0.indep_states.states:r_21                            c     0.000000E+00     8.386398E+01     1.000000E+03           
         23  traj.phases.phase0.indep_states.states:r_22                            c     0.000000E+00     9.487344E+01     1.000000E+03           
         24  traj.phases.phase0.indep_states.states:r_23                            c     0.000000E+00     9.487344E+01     1.000000E+03           
         25  traj.phases.phase0.indep_states.states:r_24                            c     0.000000E+00     1.054345E+02     1.000000E+03           
         26  traj.phases.phase0.indep_states.states:r_25                            c     0.000000E+00     1.054345E+02     1.000000E+03           
         27  traj.phases.phase0.indep_states.states:r_26                            c     0.000000E+00     1.130951E+02     1.000000E+03           
         28  traj.phases.phase0.indep_states.states:r_27                            c     0.000000E+00     1.130951E+02     1.000000E+03           
         29  traj.phases.phase0.indep_states.states:r_28                            c     0.000000E+00     1.194014E+02     1.000000E+03           
         30  traj.phases.phase0.indep_states.states:h_0                             c     0.000000E+00     2.395746E+00     2.000000E+02           
         31  traj.phases.phase0.indep_states.states:h_1                             c     0.000000E+00     2.395746E+00     2.000000E+02           
         32  traj.phases.phase0.indep_states.states:h_2                             c     0.000000E+00     2.497421E+01     2.000000E+02           
         33  traj.phases.phase0.indep_states.states:h_3                             c     0.000000E+00     2.497421E+01     2.000000E+02           
         34  traj.phases.phase0.indep_states.states:h_4                             c     0.000000E+00     5.950369E+01     2.000000E+02           
         35  traj.phases.phase0.indep_states.states:h_5                             c     0.000000E+00     5.950369E+01     2.000000E+02           
         36  traj.phases.phase0.indep_states.states:h_6                             c     0.000000E+00     8.439258E+01     2.000000E+02           
         37  traj.phases.phase0.indep_states.states:h_7                             c     0.000000E+00     8.439258E+01     2.000000E+02           
         38  traj.phases.phase0.indep_states.states:h_8                             c     0.000000E+00     8.822456E+01     2.000000E+02           
         39  traj.phases.phase0.indep_states.states:h_9                             c     0.000000E+00     8.822456E+01     2.000000E+02           
         40  traj.phases.phase0.indep_states.states:h_10                            c     0.000000E+00     7.333733E+01     2.000000E+02           
         41  traj.phases.phase0.indep_states.states:h_11                            c     0.000000E+00     7.333733E+01     2.000000E+02           
         42  traj.phases.phase0.indep_states.states:h_12                            c     0.000000E+00     7.141668E+01     2.000000E+02           
         43  traj.phases.phase0.indep_states.states:h_13                            c     0.000000E+00     7.141668E+01     2.000000E+02           
         44  traj.phases.phase0.indep_states.states:h_14                            c     0.000000E+00     7.708335E+01     2.000000E+02           
         45  traj.phases.phase0.indep_states.states:h_15                            c     0.000000E+00     7.708335E+01     2.000000E+02           
         46  traj.phases.phase0.indep_states.states:h_16                            c     0.000000E+00     8.257208E+01     2.000000E+02           
         47  traj.phases.phase0.indep_states.states:h_17                            c     0.000000E+00     8.257208E+01     2.000000E+02           
         48  traj.phases.phase0.indep_states.states:h_18                            c     0.000000E+00     8.809840E+01     2.000000E+02           
         49  traj.phases.phase0.indep_states.states:h_19                            c     0.000000E+00     8.809840E+01     2.000000E+02           
         50  traj.phases.phase0.indep_states.states:h_20                            c     0.000000E+00     9.129355E+01     2.000000E+02           
         51  traj.phases.phase0.indep_states.states:h_21                            c     0.000000E+00     9.129355E+01     2.000000E+02           
         52  traj.phases.phase0.indep_states.states:h_22                            c     0.000000E+00     9.362772E+01     2.000000E+02           
         53  traj.phases.phase0.indep_states.states:h_23                            c     0.000000E+00     9.362772E+01     2.000000E+02           
         54  traj.phases.phase0.indep_states.states:h_24                            c     0.000000E+00     1.210323E+02     2.000000E+02           
         55  traj.phases.phase0.indep_states.states:h_25                            c     0.000000E+00     1.210323E+02     2.000000E+02           
         56  traj.phases.phase0.indep_states.states:h_26                            c     0.000000E+00     1.727778E+02     2.000000E+02           
         57  traj.phases.phase0.indep_states.states:h_27                            c     0.000000E+00     1.727778E+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     2.631038E+00     1.000000E+19           
         60  traj.phases.phase0.indep_states.states:v_1                             c     1.000000E-01     2.631038E+00     1.000000E+19           
         61  traj.phases.phase0.indep_states.states:v_2                             c     1.000000E-01     3.105407E+00     1.000000E+19           
         62  traj.phases.phase0.indep_states.states:v_3                             c     1.000000E-01     3.105407E+00     1.000000E+19           
         63  traj.phases.phase0.indep_states.states:v_4                             c     1.000000E-01     2.949820E+00     1.000000E+19           
         64  traj.phases.phase0.indep_states.states:v_5                             c     1.000000E-01     2.949820E+00     1.000000E+19           
         65  traj.phases.phase0.indep_states.states:v_6                             c     1.000000E-01     2.844030E+00     1.000000E+19           
         66  traj.phases.phase0.indep_states.states:v_7                             c     1.000000E-01     2.844030E+00     1.000000E+19           
         67  traj.phases.phase0.indep_states.states:v_8                             c     1.000000E-01     3.246882E+00     1.000000E+19           
         68  traj.phases.phase0.indep_states.states:v_9                             c     1.000000E-01     3.246882E+00     1.000000E+19           
         69  traj.phases.phase0.indep_states.states:v_10                            c     1.000000E-01     3.935752E+00     1.000000E+19           
         70  traj.phases.phase0.indep_states.states:v_11                            c     1.000000E-01     3.935752E+00     1.000000E+19           
         71  traj.phases.phase0.indep_states.states:v_12                            c     1.000000E-01     4.239248E+00     1.000000E+19           
         72  traj.phases.phase0.indep_states.states:v_13                            c     1.000000E-01     4.239248E+00     1.000000E+19           
         73  traj.phases.phase0.indep_states.states:v_14                            c     1.000000E-01     4.391453E+00     1.000000E+19           
         74  traj.phases.phase0.indep_states.states:v_15                            c     1.000000E-01     4.391453E+00     1.000000E+19           
         75  traj.phases.phase0.indep_states.states:v_16                            c     1.000000E-01     4.559049E+00     1.000000E+19           
         76  traj.phases.phase0.indep_states.states:v_17                            c     1.000000E-01     4.559049E+00     1.000000E+19           
         77  traj.phases.phase0.indep_states.states:v_18                            c     1.000000E-01     4.734792E+00     1.000000E+19           
         78  traj.phases.phase0.indep_states.states:v_19                            c     1.000000E-01     4.734792E+00     1.000000E+19           
         79  traj.phases.phase0.indep_states.states:v_20                            c     1.000000E-01     4.969174E+00     1.000000E+19           
         80  traj.phases.phase0.indep_states.states:v_21                            c     1.000000E-01     4.969174E+00     1.000000E+19           
         81  traj.phases.phase0.indep_states.states:v_22                            c     1.000000E-01     5.192070E+00     1.000000E+19           
         82  traj.phases.phase0.indep_states.states:v_23                            c     1.000000E-01     5.192070E+00     1.000000E+19           
         83  traj.phases.phase0.indep_states.states:v_24                            c     1.000000E-01     4.819353E+00     1.000000E+19           
         84  traj.phases.phase0.indep_states.states:v_25                            c     1.000000E-01     4.819353E+00     1.000000E+19           
         85  traj.phases.phase0.indep_states.states:v_26                            c     1.000000E-01     3.704187E+00     1.000000E+19           
         86  traj.phases.phase0.indep_states.states:v_27                            c     1.000000E-01     3.704187E+00     1.000000E+19           
         87  traj.phases.phase0.indep_states.states:v_28                            c     1.000000E-01     2.950864E+00     1.000000E+19           
         88  traj.phases.phase0.indep_states.states:gam_0                           c    -1.500000E+00     9.837993E-02     1.500000E+00           
         89  traj.phases.phase0.indep_states.states:gam_1                           c    -1.500000E+00     9.837993E-02     1.500000E+00           
         90  traj.phases.phase0.indep_states.states:gam_2                           c    -1.500000E+00     5.982229E-01     1.500000E+00           
         91  traj.phases.phase0.indep_states.states:gam_3                           c    -1.500000E+00     5.982229E-01     1.500000E+00           
         92  traj.phases.phase0.indep_states.states:gam_4                           c    -1.500000E+00     4.576374E-01     1.500000E+00           
         93  traj.phases.phase0.indep_states.states:gam_5                           c    -1.500000E+00     4.576374E-01     1.500000E+00           
         94  traj.phases.phase0.indep_states.states:gam_6                           c    -1.500000E+00     3.202657E-01     1.500000E+00           
         95  traj.phases.phase0.indep_states.states:gam_7                           c    -1.500000E+00     3.202657E-01     1.500000E+00           
         96  traj.phases.phase0.indep_states.states:gam_8                           c    -1.500000E+00    -1.749280E-01     1.500000E+00           
         97  traj.phases.phase0.indep_states.states:gam_9                           c    -1.500000E+00    -1.749280E-01     1.500000E+00           
         98  traj.phases.phase0.indep_states.states:gam_10                          c    -1.500000E+00    -1.199618E-01     1.500000E+00           
         99  traj.phases.phase0.indep_states.states:gam_11                          c    -1.500000E+00    -1.199618E-01     1.500000E+00           
        100  traj.phases.phase0.indep_states.states:gam_12                          c    -1.500000E+00     4.664642E-02     1.500000E+00           
        101  traj.phases.phase0.indep_states.states:gam_13                          c    -1.500000E+00     4.664642E-02     1.500000E+00           
        102  traj.phases.phase0.indep_states.states:gam_14                          c    -1.500000E+00     6.015774E-02     1.500000E+00           
        103  traj.phases.phase0.indep_states.states:gam_15                          c    -1.500000E+00     6.015774E-02     1.500000E+00           
        104  traj.phases.phase0.indep_states.states:gam_16                          c    -1.500000E+00     5.603281E-02     1.500000E+00           
        105  traj.phases.phase0.indep_states.states:gam_17                          c    -1.500000E+00     5.603281E-02     1.500000E+00           
        106  traj.phases.phase0.indep_states.states:gam_18                          c    -1.500000E+00     4.944014E-02     1.500000E+00           
        107  traj.phases.phase0.indep_states.states:gam_19                          c    -1.500000E+00     4.944014E-02     1.500000E+00           
        108  traj.phases.phase0.indep_states.states:gam_20                          c    -1.500000E+00     1.041581E-02     1.500000E+00           
        109  traj.phases.phase0.indep_states.states:gam_21                          c    -1.500000E+00     1.041581E-02     1.500000E+00           
        110  traj.phases.phase0.indep_states.states:gam_22                          c    -1.500000E+00     7.776294E-02     1.500000E+00           
        111  traj.phases.phase0.indep_states.states:gam_23                          c    -1.500000E+00     7.776294E-02     1.500000E+00           
        112  traj.phases.phase0.indep_states.states:gam_24                          c    -1.500000E+00     4.658705E-01     1.500000E+00           
        113  traj.phases.phase0.indep_states.states:gam_25                          c    -1.500000E+00     4.658705E-01     1.500000E+00           
        114  traj.phases.phase0.indep_states.states:gam_26                          c    -1.500000E+00     6.282832E-01     1.500000E+00           
        115  traj.phases.phase0.indep_states.states:gam_27                          c    -1.500000E+00     6.282832E-01     1.500000E+00           
        116  traj.phases.phase0.indep_states.states:gam_28                          c    -1.500000E+00     4.516913E-20     1.500000E+00           
        117  traj.phases.phase0.indep_states.states:m_0                             c     1.000000E-02     1.884020E+01     1.000000E+02           
        118  traj.phases.phase0.indep_states.states:m_1                             c     1.000000E-02     1.884020E+01     1.000000E+02           
        119  traj.phases.phase0.indep_states.states:m_2                             c     1.000000E-02     1.863610E+01     1.000000E+02           
        120  traj.phases.phase0.indep_states.states:m_3                             c     1.000000E-02     1.863610E+01     1.000000E+02           
        121  traj.phases.phase0.indep_states.states:m_4                             c     1.000000E-02     1.847456E+01     1.000000E+02           
        122  traj.phases.phase0.indep_states.states:m_5                             c     1.000000E-02     1.847456E+01     1.000000E+02           
        123  traj.phases.phase0.indep_states.states:m_6                             c     1.000000E-02     1.835553E+01     1.000000E+02           
        124  traj.phases.phase0.indep_states.states:m_7                             c     1.000000E-02     1.835553E+01     1.000000E+02           
        125  traj.phases.phase0.indep_states.states:m_8                             c     1.000000E-02     1.825260E+01     1.000000E+02           
        126  traj.phases.phase0.indep_states.states:m_9                             c     1.000000E-02     1.825260E+01     1.000000E+02           
        127  traj.phases.phase0.indep_states.states:m_10                            c     1.000000E-02     1.811673E+01     1.000000E+02           
        128  traj.phases.phase0.indep_states.states:m_11                            c     1.000000E-02     1.811673E+01     1.000000E+02           
        129  traj.phases.phase0.indep_states.states:m_12                            c     1.000000E-02     1.794607E+01     1.000000E+02           
        130  traj.phases.phase0.indep_states.states:m_13                            c     1.000000E-02     1.794607E+01     1.000000E+02           
        131  traj.phases.phase0.indep_states.states:m_14                            c     1.000000E-02     1.777067E+01     1.000000E+02           
        132  traj.phases.phase0.indep_states.states:m_15                            c     1.000000E-02     1.777067E+01     1.000000E+02           
        133  traj.phases.phase0.indep_states.states:m_16                            c     1.000000E-02     1.759672E+01     1.000000E+02           
        134  traj.phases.phase0.indep_states.states:m_17                            c     1.000000E-02     1.759672E+01     1.000000E+02           
        135  traj.phases.phase0.indep_states.states:m_18                            c     1.000000E-02     1.742389E+01     1.000000E+02           
        136  traj.phases.phase0.indep_states.states:m_19                            c     1.000000E-02     1.742389E+01     1.000000E+02           
        137  traj.phases.phase0.indep_states.states:m_20                            c     1.000000E-02     1.725041E+01     1.000000E+02           
        138  traj.phases.phase0.indep_states.states:m_21                            c     1.000000E-02     1.725041E+01     1.000000E+02           
        139  traj.phases.phase0.indep_states.states:m_22                            c     1.000000E-02     1.707081E+01     1.000000E+02           
        140  traj.phases.phase0.indep_states.states:m_23                            c     1.000000E-02     1.707081E+01     1.000000E+02           
        141  traj.phases.phase0.indep_states.states:m_24                            c     1.000000E-02     1.691149E+01     1.000000E+02           
        142  traj.phases.phase0.indep_states.states:m_25                            c     1.000000E-02     1.691149E+01     1.000000E+02           
        143  traj.phases.phase0.indep_states.states:m_26                            c     1.000000E-02     1.683630E+01     1.000000E+02           
        144  traj.phases.phase0.indep_states.states:m_27                            c     1.000000E-02     1.683630E+01     1.000000E+02           
        145  traj.phases.phase0.indep_states.states:m_28                            c     1.000000E-02     1.681289E+01     1.000000E+02           
        146  traj.phases.phase0.control_group.indep_controls.controls:alpha_0       c    -8.000000E+00     5.418391E+00     8.000000E+00           
        147  traj.phases.phase0.control_group.indep_controls.controls:alpha_1       c    -8.000000E+00     2.640643E+00     8.000000E+00           
        148  traj.phases.phase0.control_group.indep_controls.controls:alpha_2       c    -8.000000E+00     2.026801E+00     8.000000E+00           
        149  traj.phases.phase0.control_group.indep_controls.controls:alpha_3       c    -8.000000E+00     2.026801E+00     8.000000E+00           
        150  traj.phases.phase0.control_group.indep_controls.controls:alpha_4       c    -8.000000E+00     2.090902E+00     8.000000E+00           
        151  traj.phases.phase0.control_group.indep_controls.controls:alpha_5       c    -8.000000E+00     1.346987E+00     8.000000E+00           
        152  traj.phases.phase0.control_group.indep_controls.controls:alpha_6       c    -8.000000E+00     1.346987E+00     8.000000E+00           
        153  traj.phases.phase0.control_group.indep_controls.controls:alpha_7       c    -8.000000E+00     7.741878E-01     8.000000E+00           
        154  traj.phases.phase0.control_group.indep_controls.controls:alpha_8       c    -8.000000E+00     1.351638E+00     8.000000E+00           
        155  traj.phases.phase0.control_group.indep_controls.controls:alpha_9       c    -8.000000E+00     1.351638E+00     8.000000E+00           
        156  traj.phases.phase0.control_group.indep_controls.controls:alpha_10      c    -8.000000E+00     1.880873E+00     8.000000E+00           
        157  traj.phases.phase0.control_group.indep_controls.controls:alpha_11      c    -8.000000E+00     1.163431E+00     8.000000E+00           
        158  traj.phases.phase0.control_group.indep_controls.controls:alpha_12      c    -8.000000E+00     1.163431E+00     8.000000E+00           
        159  traj.phases.phase0.control_group.indep_controls.controls:alpha_13      c    -8.000000E+00     4.812157E-01     8.000000E+00           
        160  traj.phases.phase0.control_group.indep_controls.controls:alpha_14      c    -8.000000E+00     1.116131E+00     8.000000E+00           
        161  traj.phases.phase0.control_group.indep_controls.controls:alpha_15      c    -8.000000E+00     1.116131E+00     8.000000E+00           
        162  traj.phases.phase0.control_group.indep_controls.controls:alpha_16      c    -8.000000E+00     1.991627E+00     8.000000E+00           
        163  traj.phases.phase0.control_group.indep_controls.controls:alpha_17      c    -8.000000E+00     2.031153E+00     8.000000E+00           
        164  traj.phases.phase0.control_group.indep_controls.controls:alpha_18      c    -8.000000E+00     2.031153E+00     8.000000E+00           
        165  traj.phases.phase0.control_group.indep_controls.controls:alpha_19      c    -8.000000E+00     1.687478E+00     8.000000E+00           
        166  traj.phases.phase0.control_group.indep_controls.controls:alpha_20      c    -8.000000E+00     1.413371E+00     8.000000E+00           
        167  traj.phases.phase0.control_group.indep_controls.controls:alpha_21      c    -8.000000E+00     1.413371E+00     8.000000E+00           
        168  traj.phases.phase0.control_group.indep_controls.controls:alpha_22      c    -8.000000E+00     1.243072E+00     8.000000E+00           
        169  traj.phases.phase0.control_group.indep_controls.controls:alpha_23      c    -8.000000E+00     1.210822E+00     8.000000E+00           
        170  traj.phases.phase0.control_group.indep_controls.controls:alpha_24      c    -8.000000E+00     1.210822E+00     8.000000E+00           
        171  traj.phases.phase0.control_group.indep_controls.controls:alpha_25      c    -8.000000E+00     1.243089E+00     8.000000E+00           
        172  traj.phases.phase0.control_group.indep_controls.controls:alpha_26      c    -8.000000E+00     1.266340E+00     8.000000E+00           
        173  traj.phases.phase0.control_group.indep_controls.controls:alpha_27      c    -8.000000E+00     1.266340E+00     8.000000E+00           
        174  traj.phases.phase0.control_group.indep_controls.controls:alpha_28      c    -8.000000E+00     1.260563E+00     8.000000E+00           
        175  traj.phases.phase0.control_group.indep_controls.controls:alpha_29      c    -8.000000E+00     1.205746E+00     8.000000E+00           
        176  traj.phases.phase0.control_group.indep_controls.controls:alpha_30      c    -8.000000E+00     1.205746E+00     8.000000E+00           
        177  traj.phases.phase0.control_group.indep_controls.controls:alpha_31      c    -8.000000E+00     1.152193E+00     8.000000E+00           
        178  traj.phases.phase0.control_group.indep_controls.controls:alpha_32      c    -8.000000E+00     1.150211E+00     8.000000E+00           
        179  traj.phases.phase0.control_group.indep_controls.controls:alpha_33      c    -8.000000E+00     1.150211E+00     8.000000E+00           
        180  traj.phases.phase0.control_group.indep_controls.controls:alpha_34      c    -8.000000E+00     1.360848E+00     8.000000E+00           
        181  traj.phases.phase0.control_group.indep_controls.controls:alpha_35      c    -8.000000E+00     1.945151E+00     8.000000E+00           
        182  traj.phases.phase0.control_group.indep_controls.controls:alpha_36      c    -8.000000E+00     1.945151E+00     8.000000E+00           
        183  traj.phases.phase0.control_group.indep_controls.controls:alpha_37      c    -8.000000E+00     2.754002E+00     8.000000E+00           
        184  traj.phases.phase0.control_group.indep_controls.controls:alpha_38      c    -8.000000E+00     3.638284E+00     8.000000E+00           
        185  traj.phases.phase0.control_group.indep_controls.controls:alpha_39      c    -8.000000E+00     3.638284E+00     8.000000E+00           
        186  traj.phases.phase0.control_group.indep_controls.controls:alpha_40      c    -8.000000E+00     3.954750E+00     8.000000E+00           
        187  traj.phases.phase0.control_group.indep_controls.controls:alpha_41      c    -8.000000E+00     3.060154E+00     8.000000E+00           
        188  traj.phases.phase0.control_group.indep_controls.controls:alpha_42      c    -8.000000E+00     3.060154E+00     8.000000E+00           
        189  traj.phases.phase0.control_group.indep_controls.controls:alpha_43      c    -8.000000E+00    -1.272477E-01     8.000000E+00           
        190  traj.phases.phase0.control_group.indep_controls.controls:alpha_44      c    -8.000000E+00    -6.689202E+00     8.000000E+00           

   Constraints (i - inequality, e - equality)
      Index  Name                                                               Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
          0  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    4.662268E-12    0.000000E+00              9.00000E+100
          1  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    4.107192E-12    0.000000E+00              9.00000E+100
          2  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00   -2.453570E-11    0.000000E+00              9.00000E+100
          3  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.167311E-10    0.000000E+00              9.00000E+100
          4  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.253992E-10    0.000000E+00              9.00000E+100
          5  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    2.647294E-11    0.000000E+00              9.00000E+100
          6  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    7.456129E-11    0.000000E+00              9.00000E+100
          7  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    5.193949E-11    0.000000E+00              9.00000E+100
          8  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.907109E-10    0.000000E+00              9.00000E+100
          9  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    2.495925E-10    0.000000E+00              9.00000E+100
         10  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.535982E-10    0.000000E+00              9.00000E+100
         11  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.489949E-10    0.000000E+00              9.00000E+100
         12  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    4.488672E-10    0.000000E+00              9.00000E+100
         13  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    2.538022E-10    0.000000E+00              9.00000E+100
         14  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.435884E-10    0.000000E+00              9.00000E+100
         15  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.565095E-11    0.000000E+00              9.00000E+100
         16  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.135879E-10    0.000000E+00              9.00000E+100
         17  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    3.232555E-09    0.000000E+00              9.00000E+100
         18  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    3.208279E-10    0.000000E+00              9.00000E+100
         19  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -7.427527E-10    0.000000E+00              9.00000E+100
         20  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -3.495012E-11    0.000000E+00              9.00000E+100
         21  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    6.413324E-11    0.000000E+00              9.00000E+100
         22  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.431680E-10    0.000000E+00              9.00000E+100
         23  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.642356E-09    0.000000E+00              9.00000E+100
         24  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.715788E-09    0.000000E+00              9.00000E+100
         25  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    3.621424E-11    0.000000E+00              9.00000E+100
         26  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    5.067708E-10    0.000000E+00              9.00000E+100
         27  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    5.140750E-09    0.000000E+00              9.00000E+100
         28  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.256958E-09    0.000000E+00              9.00000E+100
         29  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -8.230625E-10    0.000000E+00              9.00000E+100
         30  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.432782E-12    0.000000E+00              9.00000E+100
         31  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.786044E-11    0.000000E+00              9.00000E+100
         32  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.304011E-10    0.000000E+00              9.00000E+100
         33  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    6.472933E-10    0.000000E+00              9.00000E+100
         34  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.038933E-10    0.000000E+00              9.00000E+100
         35  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.932715E-11    0.000000E+00              9.00000E+100
         36  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.712761E-11    0.000000E+00              9.00000E+100
         37  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    7.736639E-12    0.000000E+00              9.00000E+100
         38  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.652463E-11    0.000000E+00              9.00000E+100
         39  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.897825E-10    0.000000E+00              9.00000E+100
         40  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    8.845637E-11    0.000000E+00              9.00000E+100
         41  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.012925E-10    0.000000E+00              9.00000E+100
         42  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    7.146207E-11    0.000000E+00              9.00000E+100
         43  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.954924E-11    0.000000E+00              9.00000E+100
         44  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.161582E-10    0.000000E+00              9.00000E+100
         45  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    3.791915E-13    0.000000E+00              9.00000E+100
         46  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.715214E-11    0.000000E+00              9.00000E+100
         47  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    1.194026E-11    0.000000E+00              9.00000E+100
         48  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -4.760525E-10    0.000000E+00              9.00000E+100
         49  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    1.395513E-10    0.000000E+00              9.00000E+100
         50  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -3.289734E-11    0.000000E+00              9.00000E+100
         51  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.400947E-11    0.000000E+00              9.00000E+100
         52  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -2.856607E-12    0.000000E+00              9.00000E+100
         53  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    3.128923E-12    0.000000E+00              9.00000E+100
         54  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.448719E-10    0.000000E+00              9.00000E+100
         55  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    6.194241E-12    0.000000E+00              9.00000E+100
         56  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -6.670487E-11    0.000000E+00              9.00000E+100
         57  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -7.641094E-11    0.000000E+00              9.00000E+100
         58  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -4.836387E-11    0.000000E+00              9.00000E+100
         59  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.704162E-11    0.000000E+00              9.00000E+100
         60  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -3.208264E-14    0.000000E+00              9.00000E+100
         61  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -1.069549E-13    0.000000E+00              9.00000E+100
         62  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    1.328647E-12    0.000000E+00              9.00000E+100
         63  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    5.527540E-12    0.000000E+00              9.00000E+100
         64  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    5.299584E-13    0.000000E+00              9.00000E+100
         65  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    7.335258E-13    0.000000E+00              9.00000E+100
         66  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -2.718965E-14    0.000000E+00              9.00000E+100
         67  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -1.102937E-13    0.000000E+00              9.00000E+100
         68  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -2.040663E-13    0.000000E+00              9.00000E+100
         69  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -1.348200E-12    0.000000E+00              9.00000E+100
         70  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -2.447453E-13    0.000000E+00              9.00000E+100
         71  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -4.247880E-13    0.000000E+00              9.00000E+100
         72  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    1.695429E-12    0.000000E+00              9.00000E+100
         73  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    1.016765E-11    0.000000E+00              9.00000E+100
         74  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    1.116039E-12    0.000000E+00              9.00000E+100
         75  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         76  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         77  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    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:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         90  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         91  traj.phases.phase0.continuity_comp.defect_states:h                    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:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        104  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        105  traj.phases.phase0.continuity_comp.defect_states:v                    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:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        118  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        119  traj.phases.phase0.continuity_comp.defect_states:gam                  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:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        132  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        133  traj.phases.phase0.continuity_comp.defect_states:m                    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_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        146  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        147  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        148  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        149  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        150  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        151  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        152  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        153  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        154  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        155  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        156  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        157  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        158  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        159  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    6.745845E-13    0.000000E+00              9.00000E+100
        160  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -4.497230E-13    0.000000E+00              9.00000E+100
        161  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        162  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    4.497230E-13    0.000000E+00              9.00000E+100
        163  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    2.248615E-13    0.000000E+00              9.00000E+100
        164  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    1.011877E-12    0.000000E+00              9.00000E+100
        165  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    2.810769E-13    0.000000E+00              9.00000E+100
        166  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -4.989115E-13    0.000000E+00              9.00000E+100
        167  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        168  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -1.686461E-13    0.000000E+00              9.00000E+100
        169  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -8.924191E-13    0.000000E+00              9.00000E+100
        170  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -4.497230E-13    0.000000E+00              9.00000E+100
        171  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    4.497230E-13    0.000000E+00              9.00000E+100
        172  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    4.497230E-13    0.000000E+00              9.00000E+100
        173  traj.phases.phase0.final_boundary_constraints.final_value:h           e   2.000000E+01    2.000000E+01    2.000000E+01              9.00000E+100
        174  traj.phases.phase0.final_boundary_constraints.final_value:mach        e   1.000000E+00    1.000000E+00    1.000000E+00              9.00000E+100
        175  traj.phases.phase0.final_boundary_constraints.final_value:gam         e   0.000000E+00    4.516913E-20    0.000000E+00              9.00000E+100
        176  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    5.000000E-03    1.000000E+00         l    9.00000E+100
        177  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    5.000000E-03    1.000000E+00         l    9.00000E+100
        178  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    1.197873E-02    1.000000E+00              9.00000E+100
        179  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    1.197873E-02    1.000000E+00              9.00000E+100
        180  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.829992E-02    1.000000E+00              9.00000E+100
        181  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    1.248710E-01    1.000000E+00              9.00000E+100
        182  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    1.248710E-01    1.000000E+00              9.00000E+100
        183  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    2.172110E-01    1.000000E+00              9.00000E+100
        184  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    2.975184E-01    1.000000E+00              9.00000E+100
        185  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    2.975184E-01    1.000000E+00              9.00000E+100
        186  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    3.652492E-01    1.000000E+00              9.00000E+100
        187  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.219629E-01    1.000000E+00              9.00000E+100
        188  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.219629E-01    1.000000E+00              9.00000E+100
        189  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.512623E-01    1.000000E+00              9.00000E+100
        190  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.411228E-01    1.000000E+00              9.00000E+100
        191  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.411228E-01    1.000000E+00              9.00000E+100
        192  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.026345E-01    1.000000E+00              9.00000E+100
        193  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    3.666867E-01    1.000000E+00              9.00000E+100
        194  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    3.666867E-01    1.000000E+00              9.00000E+100
        195  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    3.528562E-01    1.000000E+00              9.00000E+100
        196  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    3.570834E-01    1.000000E+00              9.00000E+100
        197  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    3.570834E-01    1.000000E+00              9.00000E+100
        198  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    3.703542E-01    1.000000E+00              9.00000E+100
        199  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    3.854167E-01    1.000000E+00              9.00000E+100
        200  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    3.854167E-01    1.000000E+00              9.00000E+100
        201  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    3.992560E-01    1.000000E+00              9.00000E+100
        202  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.128604E-01    1.000000E+00              9.00000E+100
        203  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.128604E-01    1.000000E+00              9.00000E+100
        204  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.269642E-01    1.000000E+00              9.00000E+100
        205  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.404920E-01    1.000000E+00              9.00000E+100
        206  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.404920E-01    1.000000E+00              9.00000E+100
        207  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.509405E-01    1.000000E+00              9.00000E+100
        208  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.564678E-01    1.000000E+00              9.00000E+100
        209  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.564678E-01    1.000000E+00              9.00000E+100
        210  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.575559E-01    1.000000E+00              9.00000E+100
        211  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.681386E-01    1.000000E+00              9.00000E+100
        212  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    4.681386E-01    1.000000E+00              9.00000E+100
        213  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    5.128653E-01    1.000000E+00              9.00000E+100
        214  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    6.051616E-01    1.000000E+00              9.00000E+100
        215  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    6.051616E-01    1.000000E+00              9.00000E+100
        216  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    7.343592E-01    1.000000E+00              9.00000E+100
        217  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    8.638891E-01    1.000000E+00              9.00000E+100
        218  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    8.638891E-01    1.000000E+00              9.00000E+100
        219  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    9.613416E-01    1.000000E+00              9.00000E+100
        220  traj.phases.phase0.path_constraints.path:h                            i   5.000000E-03    1.000000E+00    1.000000E+00         u    9.00000E+100
        221  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    4.000084E-01    1.800000E+00              9.00000E+100
        222  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    5.894301E-01    1.800000E+00              9.00000E+100
        223  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    7.752800E-01    1.800000E+00              9.00000E+100
        224  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    7.752800E-01    1.800000E+00              9.00000E+100
        225  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    9.007171E-01    1.800000E+00              9.00000E+100
        226  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    9.394303E-01    1.800000E+00              9.00000E+100
        227  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    9.394303E-01    1.800000E+00              9.00000E+100
        228  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    9.347162E-01    1.800000E+00              9.00000E+100
        229  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    9.316401E-01    1.800000E+00              9.00000E+100
        230  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    9.316401E-01    1.800000E+00              9.00000E+100
        231  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    9.276698E-01    1.800000E+00              9.00000E+100
        232  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    9.288500E-01    1.800000E+00              9.00000E+100
        233  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    9.288500E-01    1.800000E+00              9.00000E+100
        234  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    9.731568E-01    1.800000E+00              9.00000E+100
        235  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.066127E+00    1.800000E+00              9.00000E+100
        236  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.066127E+00    1.800000E+00              9.00000E+100
        237  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.175772E+00    1.800000E+00              9.00000E+100
        238  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.266053E+00    1.800000E+00              9.00000E+100
        239  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.266053E+00    1.800000E+00              9.00000E+100
        240  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.323177E+00    1.800000E+00              9.00000E+100
        241  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.360155E+00    1.800000E+00              9.00000E+100
        242  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.360155E+00    1.800000E+00              9.00000E+100
        243  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.389953E+00    1.800000E+00              9.00000E+100
        244  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.419849E+00    1.800000E+00              9.00000E+100
        245  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.419849E+00    1.800000E+00              9.00000E+100
        246  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.452024E+00    1.800000E+00              9.00000E+100
        247  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.485207E+00    1.800000E+00              9.00000E+100
        248  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.485207E+00    1.800000E+00              9.00000E+100
        249  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.518859E+00    1.800000E+00              9.00000E+100
        250  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.554413E+00    1.800000E+00              9.00000E+100
        251  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.554413E+00    1.800000E+00              9.00000E+100
        252  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.594253E+00    1.800000E+00              9.00000E+100
        253  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.638746E+00    1.800000E+00              9.00000E+100
        254  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.638746E+00    1.800000E+00              9.00000E+100
        255  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.685035E+00    1.800000E+00              9.00000E+100
        256  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.717958E+00    1.800000E+00              9.00000E+100
        257  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.717958E+00    1.800000E+00              9.00000E+100
        258  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.716158E+00    1.800000E+00              9.00000E+100
        259  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.633328E+00    1.800000E+00              9.00000E+100
        260  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.633328E+00    1.800000E+00              9.00000E+100
        261  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.457262E+00    1.800000E+00              9.00000E+100
        262  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.255387E+00    1.800000E+00              9.00000E+100
        263  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.255387E+00    1.800000E+00              9.00000E+100
        264  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.080961E+00    1.800000E+00              9.00000E+100
        265  traj.phases.phase0.path_constraints.path:mach                         i   1.000000E-01    1.000000E+00    1.800000E+00              9.00000E+100

--------------------------------------------------------------------------------


Simulating trajectory traj
Done simulating trajectory traj

References


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