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 free-body-diagram of the min-time-climb problem.

The vehicle dynamics are given by

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

The initial conditions are

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

and the final conditions are

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

The ODE System: min_time_climb_ode.py#

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

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:check_config:checking out_of_order
INFO: checking system
INFO:check_config:checking system
INFO: checking solvers
INFO:check_config:checking solvers
INFO: checking dup_inputs
INFO:check_config:checking dup_inputs
INFO: checking missing_recorders
INFO:check_config:checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
WARNING:check_config:The Problem has no recorder of any kind attached
INFO: checking unserializable_options
INFO:check_config:checking unserializable_options
INFO: checking comp_has_no_outputs
INFO:check_config:checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
INFO:check_config:checking auto_ivc_warnings
Model viewer data has already been recorded for Driver.
INFO: checking out_of_order
INFO:check_config:checking out_of_order
INFO: checking system
INFO:check_config:checking system
INFO: checking solvers
INFO:check_config:checking solvers
INFO: checking dup_inputs
INFO:check_config:checking dup_inputs
INFO: checking missing_recorders
INFO:check_config:checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
WARNING:check_config:The Problem has no recorder of any kind attached
INFO: checking unserializable_options
INFO:check_config:checking unserializable_options
INFO: checking comp_has_no_outputs
INFO:check_config:checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
INFO:check_config:checking auto_ivc_warnings
Full total jacobian was computed 3 times, taking 0.251576 seconds.
Total jacobian shape: (181, 191) 
Jacobian shape: (181, 191)  ( 8.81% nonzero)
FWD solves: 25   REV solves: 0
Total colors vs. total size: 25 vs 191  (86.9% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.251576 sec.
Time to compute coloring: 0.306216 sec.
Memory to compute coloring: 1.878906 MB.
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/core/total_jac.py:1567: DerivativesWarning:Constraints or objectives [('traj.phases.phase0.timeseries.states:h', inds=[(0, 0)]), ('traj.phases.phase0.timeseries.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:                   12.0925
       User Objective Time :       2.2117
       User Sensitivity Time :     2.3869
       Interface Time :            3.2931
       Opt Solver Time:            4.2008
    Calls to Objective Function :     131
    Calls to Sens Function :          108


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

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

   Constraints (i - inequality, e - equality)
      Index  Name                                                               Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
          0  traj.phases.phase0->final_boundary_constraint->h                      e   2.000000E+01    2.000000E+01    2.000000E+01              9.00000E+100
          1  traj.phases.phase0->final_boundary_constraint->mach                   e   1.000000E+00    1.000000E+00    1.000000E+00              9.00000E+100
          2  traj.phases.phase0->final_boundary_constraint->gam                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          3  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.584597E-10    0.000000E+00              9.00000E+100
          4  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00   -2.415745E-11    0.000000E+00              9.00000E+100
          5  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    6.957332E-10    0.000000E+00              9.00000E+100
          6  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    4.010502E-10    0.000000E+00              9.00000E+100
          7  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    3.194947E-09    0.000000E+00              9.00000E+100
          8  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    4.847693E-10    0.000000E+00              9.00000E+100
          9  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    3.020406E-09    0.000000E+00              9.00000E+100
         10  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    2.301455E-09    0.000000E+00              9.00000E+100
         11  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    9.152259E-10    0.000000E+00              9.00000E+100
         12  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    6.912010E-10    0.000000E+00              9.00000E+100
         13  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.936923E-10    0.000000E+00              9.00000E+100
         14  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.069429E-10    0.000000E+00              9.00000E+100
         15  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00   -2.134962E-11    0.000000E+00              9.00000E+100
         16  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    8.720528E-10    0.000000E+00              9.00000E+100
         17  traj.phases.phase0.collocation_constraint.defects:r                   e   0.000000E+00    1.393463E-10    0.000000E+00              9.00000E+100
         18  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    7.098596E-10    0.000000E+00              9.00000E+100
         19  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    7.136203E-09    0.000000E+00              9.00000E+100
         20  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    5.237474E-10    0.000000E+00              9.00000E+100
         21  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.733429E-09    0.000000E+00              9.00000E+100
         22  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    4.110917E-08    0.000000E+00              9.00000E+100
         23  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.676348E-09    0.000000E+00              9.00000E+100
         24  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -2.944404E-08    0.000000E+00              9.00000E+100
         25  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    5.821975E-09    0.000000E+00              9.00000E+100
         26  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -2.788358E-09    0.000000E+00              9.00000E+100
         27  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.861896E-09    0.000000E+00              9.00000E+100
         28  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -2.061940E-09    0.000000E+00              9.00000E+100
         29  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    4.536093E-10    0.000000E+00              9.00000E+100
         30  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    6.582518E-09    0.000000E+00              9.00000E+100
         31  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.989606E-09    0.000000E+00              9.00000E+100
         32  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.409820E-09    0.000000E+00              9.00000E+100
         33  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.032148E-11    0.000000E+00              9.00000E+100
         34  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.340993E-09    0.000000E+00              9.00000E+100
         35  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.680164E-10    0.000000E+00              9.00000E+100
         36  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.996181E-10    0.000000E+00              9.00000E+100
         37  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.754336E-10    0.000000E+00              9.00000E+100
         38  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.325291E-09    0.000000E+00              9.00000E+100
         39  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.187982E-09    0.000000E+00              9.00000E+100
         40  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -1.361550E-12    0.000000E+00              9.00000E+100
         41  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.803362E-10    0.000000E+00              9.00000E+100
         42  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.203308E-10    0.000000E+00              9.00000E+100
         43  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.395591E-10    0.000000E+00              9.00000E+100
         44  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.006160E-10    0.000000E+00              9.00000E+100
         45  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.067062E-10    0.000000E+00              9.00000E+100
         46  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.689513E-10    0.000000E+00              9.00000E+100
         47  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.436010E-10    0.000000E+00              9.00000E+100
         48  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    1.986516E-11    0.000000E+00              9.00000E+100
         49  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.064342E-09    0.000000E+00              9.00000E+100
         50  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -4.928038E-11    0.000000E+00              9.00000E+100
         51  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    2.048956E-12    0.000000E+00              9.00000E+100
         52  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    9.780965E-10    0.000000E+00              9.00000E+100
         53  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.048589E-09    0.000000E+00              9.00000E+100
         54  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    4.401948E-10    0.000000E+00              9.00000E+100
         55  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.153268E-10    0.000000E+00              9.00000E+100
         56  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -4.020872E-10    0.000000E+00              9.00000E+100
         57  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -3.189491E-10    0.000000E+00              9.00000E+100
         58  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    6.674056E-11    0.000000E+00              9.00000E+100
         59  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -2.630549E-13    0.000000E+00              9.00000E+100
         60  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    1.154864E-10    0.000000E+00              9.00000E+100
         61  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00   -1.887596E-10    0.000000E+00              9.00000E+100
         62  traj.phases.phase0.collocation_constraint.defects:gam                 e   0.000000E+00    4.729507E-11    0.000000E+00              9.00000E+100
         63  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -1.150061E-12    0.000000E+00              9.00000E+100
         64  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -6.636628E-12    0.000000E+00              9.00000E+100
         65  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -4.250920E-12    0.000000E+00              9.00000E+100
         66  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    8.791901E-13    0.000000E+00              9.00000E+100
         67  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    3.072270E-11    0.000000E+00              9.00000E+100
         68  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    1.247069E-10    0.000000E+00              9.00000E+100
         69  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -9.314056E-12    0.000000E+00              9.00000E+100
         70  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -2.781831E-12    0.000000E+00              9.00000E+100
         71  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -2.104544E-12    0.000000E+00              9.00000E+100
         72  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -6.094560E-14    0.000000E+00              9.00000E+100
         73  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -9.031774E-13    0.000000E+00              9.00000E+100
         74  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00   -1.867060E-12    0.000000E+00              9.00000E+100
         75  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    1.378185E-12    0.000000E+00              9.00000E+100
         76  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    1.089351E-11    0.000000E+00              9.00000E+100
         77  traj.phases.phase0.collocation_constraint.defects:m                   e   0.000000E+00    3.158357E-13    0.000000E+00              9.00000E+100
         78  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         79  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         80  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         81  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         82  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         83  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         84  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         85  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         86  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         87  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         88  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         89  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         90  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         91  traj.phases.phase0.continuity_comp.defect_states:r                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         92  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         93  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         94  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         95  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         96  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         97  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         98  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         99  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        100  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        101  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        102  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        103  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        104  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        105  traj.phases.phase0.continuity_comp.defect_states:h                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        106  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        107  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        108  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        109  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        110  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        111  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        112  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        113  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        114  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        115  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        116  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        117  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        118  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        119  traj.phases.phase0.continuity_comp.defect_states:v                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        120  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        121  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        122  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        123  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        124  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        125  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        126  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00   -6.938894E-18    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   -1.734723E-18    0.000000E+00              9.00000E+100
        131  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        132  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        133  traj.phases.phase0.continuity_comp.defect_states:gam                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        134  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        135  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        136  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        137  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        138  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        139  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        140  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        141  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        142  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        143  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        144  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        145  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        146  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        147  traj.phases.phase0.continuity_comp.defect_states:m                    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        148  traj.phases.phase0.continuity_comp.defect_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_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        160  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        161  traj.phases.phase0.continuity_comp.defect_controls:alpha              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    1.354159E-12    0.000000E+00              9.00000E+100
        163  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        164  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -2.256932E-13    0.000000E+00              9.00000E+100
        165  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    6.770797E-13    0.000000E+00              9.00000E+100
        166  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    2.256932E-13    0.000000E+00              9.00000E+100
        167  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -3.385399E-13    0.000000E+00              9.00000E+100
        168  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -2.821166E-13    0.000000E+00              9.00000E+100
        169  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -5.007569E-13    0.000000E+00              9.00000E+100
        170  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -1.001514E-12    0.000000E+00              9.00000E+100
        171  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    1.156678E-12    0.000000E+00              9.00000E+100
        172  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    1.234260E-13    0.000000E+00              9.00000E+100
        173  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    4.513865E-13    0.000000E+00              9.00000E+100
        174  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -1.128466E-12    0.000000E+00              9.00000E+100
        175  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -2.256932E-12    0.000000E+00              9.00000E+100
        176  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    5.000000E-03    1.000000E+00         l    9.00000E+100
        177  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    5.000000E-03    1.000000E+00         l    9.00000E+100
        178  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    1.223116E-02    1.000000E+00              9.00000E+100
        179  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    1.223116E-02    1.000000E+00              9.00000E+100
        180  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.913506E-02    1.000000E+00              9.00000E+100
        181  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    1.261712E-01    1.000000E+00              9.00000E+100
        182  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    1.261712E-01    1.000000E+00              9.00000E+100
        183  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    2.186518E-01    1.000000E+00              9.00000E+100
        184  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    2.989578E-01    1.000000E+00              9.00000E+100
        185  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    2.989578E-01    1.000000E+00              9.00000E+100
        186  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.667072E-01    1.000000E+00              9.00000E+100
        187  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.234316E-01    1.000000E+00              9.00000E+100
        188  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.234316E-01    1.000000E+00              9.00000E+100
        189  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.525688E-01    1.000000E+00              9.00000E+100
        190  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.419970E-01    1.000000E+00              9.00000E+100
        191  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.419970E-01    1.000000E+00              9.00000E+100
        192  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.029582E-01    1.000000E+00              9.00000E+100
        193  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.667178E-01    1.000000E+00              9.00000E+100
        194  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.667178E-01    1.000000E+00              9.00000E+100
        195  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.529703E-01    1.000000E+00              9.00000E+100
        196  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.573729E-01    1.000000E+00              9.00000E+100
        197  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.573729E-01    1.000000E+00              9.00000E+100
        198  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.707172E-01    1.000000E+00              9.00000E+100
        199  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.857635E-01    1.000000E+00              9.00000E+100
        200  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.857635E-01    1.000000E+00              9.00000E+100
        201  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    3.995497E-01    1.000000E+00              9.00000E+100
        202  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.131152E-01    1.000000E+00              9.00000E+100
        203  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.131152E-01    1.000000E+00              9.00000E+100
        204  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.272108E-01    1.000000E+00              9.00000E+100
        205  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.407678E-01    1.000000E+00              9.00000E+100
        206  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.407678E-01    1.000000E+00              9.00000E+100
        207  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.513144E-01    1.000000E+00              9.00000E+100
        208  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.569471E-01    1.000000E+00              9.00000E+100
        209  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.569471E-01    1.000000E+00              9.00000E+100
        210  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.579603E-01    1.000000E+00              9.00000E+100
        211  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.681077E-01    1.000000E+00              9.00000E+100
        212  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    4.681077E-01    1.000000E+00              9.00000E+100
        213  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    5.120673E-01    1.000000E+00              9.00000E+100
        214  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    6.037812E-01    1.000000E+00              9.00000E+100
        215  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    6.037812E-01    1.000000E+00              9.00000E+100
        216  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    7.330585E-01    1.000000E+00              9.00000E+100
        217  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    8.631062E-01    1.000000E+00              9.00000E+100
        218  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    8.631062E-01    1.000000E+00              9.00000E+100
        219  traj.phases.phase0->path_constraint->h                                i   5.000000E-03    9.610986E-01    1.000000E+00              9.00000E+100
        220  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    4.000084E-01    1.800000E+00              9.00000E+100
        221  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    5.901466E-01    1.800000E+00              9.00000E+100
        222  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    7.761596E-01    1.800000E+00              9.00000E+100
        223  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    7.761596E-01    1.800000E+00              9.00000E+100
        224  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.011669E-01    1.800000E+00              9.00000E+100
        225  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.395412E-01    1.800000E+00              9.00000E+100
        226  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.395412E-01    1.800000E+00              9.00000E+100
        227  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.347896E-01    1.800000E+00              9.00000E+100
        228  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.317467E-01    1.800000E+00              9.00000E+100
        229  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.317467E-01    1.800000E+00              9.00000E+100
        230  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.276685E-01    1.800000E+00              9.00000E+100
        231  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.287320E-01    1.800000E+00              9.00000E+100
        232  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.287320E-01    1.800000E+00              9.00000E+100
        233  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    9.732941E-01    1.800000E+00              9.00000E+100
        234  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.066912E+00    1.800000E+00              9.00000E+100
        235  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.066912E+00    1.800000E+00              9.00000E+100
        236  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.177187E+00    1.800000E+00              9.00000E+100
        237  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.267651E+00    1.800000E+00              9.00000E+100
        238  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.267651E+00    1.800000E+00              9.00000E+100
        239  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.324568E+00    1.800000E+00              9.00000E+100
        240  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.361322E+00    1.800000E+00              9.00000E+100
        241  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.361322E+00    1.800000E+00              9.00000E+100
        242  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.391018E+00    1.800000E+00              9.00000E+100
        243  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.420882E+00    1.800000E+00              9.00000E+100
        244  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.420882E+00    1.800000E+00              9.00000E+100
        245  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.453028E+00    1.800000E+00              9.00000E+100
        246  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.486138E+00    1.800000E+00              9.00000E+100
        247  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.486138E+00    1.800000E+00              9.00000E+100
        248  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.519663E+00    1.800000E+00              9.00000E+100
        249  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.555025E+00    1.800000E+00              9.00000E+100
        250  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.555025E+00    1.800000E+00              9.00000E+100
        251  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.594583E+00    1.800000E+00              9.00000E+100
        252  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.638810E+00    1.800000E+00              9.00000E+100
        253  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.638810E+00    1.800000E+00              9.00000E+100
        254  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.685047E+00    1.800000E+00              9.00000E+100
        255  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.718235E+00    1.800000E+00              9.00000E+100
        256  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.718235E+00    1.800000E+00              9.00000E+100
        257  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.716946E+00    1.800000E+00              9.00000E+100
        258  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.635776E+00    1.800000E+00              9.00000E+100
        259  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.635776E+00    1.800000E+00              9.00000E+100
        260  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.459658E+00    1.800000E+00              9.00000E+100
        261  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.256960E+00    1.800000E+00              9.00000E+100
        262  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.256960E+00    1.800000E+00              9.00000E+100
        263  traj.phases.phase0->path_constraint->mach                             i   1.000000E-01    1.081436E+00    1.800000E+00              9.00000E+100

--------------------------------------------------------------------------------
/usr/share/miniconda/envs/test/lib/python3.10/site-packages/openmdao/visualization/opt_report/opt_report.py:666: UserWarning: Attempting to set identical low and high ylims makes transformation singular; automatically expanding.
  ax.set_ylim([ymin_plot, ymax_plot])
Simulating trajectory traj
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.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=sol, p_sim=sim)

plt.show()
../../_images/min_time_climb_6_0.png

References#

Bry99

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