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Two-Burn Orbit Raise

This example demonstrates the use of a Trajectory to encapsulate a three-phase orbit raising maneuver with a burn-coast-burn phase sequence. This example is based on the problem provided in Enright1.

The dynamics are given by

\begin{align} \frac{dr}{dt} &= v_r \\ \frac{d\theta}{dt} &= \frac{v_\theta}{r} \\ \frac{dv_r}{dt} &= \frac{v^2_\theta}{r} - \frac{1}{r^2} + a_{thrust} \sin u_1 \\ \frac{dv_\theta}{dt} &= - \frac{v_r v_\theta}{r} + a_{thrust} \cos u_1 \\ \frac{da_{thrust}}{dt} &= \frac{a^2_{thrust}}{c} \\ \frac{d \Delta v}{dt} &= a_{thrust} \end{align}

The initial conditions are

\begin{align} r &= 1 \rm{\,DU} \\ \theta &= 0 \rm{\,rad} \\ v_r &= 0 \rm{\,DU/TU}\\ v_\theta &= 1 \rm{\,DU/TU}\\ a_{thrust} &= 0.1 \rm{\,DU/TU^2}\\ \Delta v &= 0 \rm{\,DU/TU} \end{align}

and the final conditions are

\begin{align} r &= 3 \rm{\,DU} \\ \theta &= \rm{free} \\ v_r &= 0 \rm{\,DU/TU}\\ v_\theta &= \sqrt{\frac{1}{3}} \rm{\,DU/TU}\\ a_{thrust} &= \rm{free}\\ \Delta v &= \rm{free} \end{align}

Building and running the problem

The following code instantiates our problem, our trajectory, three phases, and links them accordingly. The spacecraft initial position, velocity, and acceleration magnitude are fixed. The objective is to minimize the delta-V needed to raise the spacecraft into a circular orbit at 3 Earth radii.

Note the call to link_phases which provides time, position, velocity, and delta-V continuity across all phases, and acceleration continuity between the first and second burn phases. Acceleration is 0 during the coast phase. Alternatively, we could have specified a different ODE for the coast phase, as in the example.

This example runs inconsistently with SLSQP but is solved handily by SNOPT.

import numpy as np
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.finite_burn_orbit_raise.finite_burn_eom import FiniteBurnODE

p = om.Problem(model=om.Group())

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

traj = dm.Trajectory()

traj.add_parameter('c', opt=False, val=1.5, units='DU/TU',
                   targets={'burn1': ['c'], 'coast': ['c'], 'burn2': ['c']})

# First Phase (burn)

burn1 = dm.Phase(ode_class=FiniteBurnODE,
                 transcription=dm.GaussLobatto(num_segments=5, order=3, compressed=False))

burn1 = traj.add_phase('burn1', burn1)

burn1.set_time_options(fix_initial=True, duration_bounds=(.5, 10), units='TU')
burn1.add_state('r', fix_initial=True, fix_final=False, defect_scaler=100.0,
                rate_source='r_dot', units='DU')
burn1.add_state('theta', fix_initial=True, fix_final=False, defect_scaler=100.0,
                rate_source='theta_dot', units='rad')
burn1.add_state('vr', fix_initial=True, fix_final=False, defect_scaler=100.0,
                rate_source='vr_dot', units='DU/TU')
burn1.add_state('vt', fix_initial=True, fix_final=False, defect_scaler=100.0,
                rate_source='vt_dot', units='DU/TU')
burn1.add_state('accel', fix_initial=True, fix_final=False,
                rate_source='at_dot', units='DU/TU**2')
burn1.add_state('deltav', fix_initial=True, fix_final=False,
                rate_source='deltav_dot', units='DU/TU')
burn1.add_control('u1', rate_continuity=True, rate2_continuity=True, units='deg',
                  scaler=0.01, rate_continuity_scaler=0.001, rate2_continuity_scaler=0.001,
                  lower=-30, upper=30)
# Second Phase (Coast)
coast = dm.Phase(ode_class=FiniteBurnODE,
                 transcription=dm.GaussLobatto(num_segments=5, order=3, compressed=False))

coast.set_time_options(initial_bounds=(0.5, 20), duration_bounds=(.5, 50), duration_ref=50,
                       units='TU')
coast.add_state('r', fix_initial=False, fix_final=False, defect_scaler=100.0,
                rate_source='r_dot', targets=['r'], units='DU')
coast.add_state('theta', fix_initial=False, fix_final=False, defect_scaler=100.0,
                rate_source='theta_dot', targets=['theta'], units='rad')
coast.add_state('vr', fix_initial=False, fix_final=False, defect_scaler=100.0,
                rate_source='vr_dot', targets=['vr'], units='DU/TU')
coast.add_state('vt', fix_initial=False, fix_final=False, defect_scaler=100.0,
                rate_source='vt_dot', targets=['vt'], units='DU/TU')
coast.add_state('accel', fix_initial=True, fix_final=True,
                rate_source='at_dot', targets=['accel'], units='DU/TU**2')
coast.add_state('deltav', fix_initial=False, fix_final=False,
                rate_source='deltav_dot', units='DU/TU')

coast.add_parameter('u1', opt=False, val=0.0, units='deg', targets=['u1'])

# Third Phase (burn)
burn2 = dm.Phase(ode_class=FiniteBurnODE,
                 transcription=dm.GaussLobatto(num_segments=5, order=3, compressed=False))

traj.add_phase('coast', coast)
traj.add_phase('burn2', burn2)

burn2.set_time_options(initial_bounds=(0.5, 50), duration_bounds=(.5, 10), initial_ref=10,
                       units='TU')
burn2.add_state('r', fix_initial=False, fix_final=True, defect_scaler=100.0,
                rate_source='r_dot', units='DU')
burn2.add_state('theta', fix_initial=False, fix_final=False, defect_scaler=100.0,
                rate_source='theta_dot', units='rad')
burn2.add_state('vr', fix_initial=False, fix_final=True, defect_scaler=1000.0,
                rate_source='vr_dot', units='DU/TU')
burn2.add_state('vt', fix_initial=False, fix_final=True, defect_scaler=1000.0,
                rate_source='vt_dot', units='DU/TU')
burn2.add_state('accel', fix_initial=False, fix_final=False, defect_scaler=1.0,
                rate_source='at_dot', units='DU/TU**2')
burn2.add_state('deltav', fix_initial=False, fix_final=False, defect_scaler=1.0,
                rate_source='deltav_dot', units='DU/TU')

burn2.add_objective('deltav', loc='final', scaler=100.0)

burn2.add_control('u1', rate_continuity=True, rate2_continuity=True, units='deg',
                  scaler=0.01, lower=-90, upper=90)

burn1.add_timeseries_output('pos_x')
coast.add_timeseries_output('pos_x')
burn2.add_timeseries_output('pos_x')

burn1.add_timeseries_output('pos_y')
coast.add_timeseries_output('pos_y')
burn2.add_timeseries_output('pos_y')

# Link Phases
traj.link_phases(phases=['burn1', 'coast', 'burn2'],
                 vars=['time', 'r', 'theta', 'vr', 'vt', 'deltav'])

traj.link_phases(phases=['burn1', 'burn2'], vars=['accel'])

p.model.add_subsystem('traj', subsys=traj)

# Finish Problem Setup

# Needed to move the direct solver down into the phases for use with MPI.
#  - After moving down, used fewer iterations (about 30 less)

p.driver.add_recorder(om.SqliteRecorder('two_burn_orbit_raise_example.db'))

p.setup(check=True, mode='fwd')

# Set Initial Guesses
p.set_val('traj.parameters:c', value=1.5, units='DU/TU')

burn1 = p.model.traj.phases.burn1
burn2 = p.model.traj.phases.burn2
coast = p.model.traj.phases.coast

p.set_val('traj.burn1.t_initial', value=0.0)
p.set_val('traj.burn1.t_duration', value=2.25)
p.set_val('traj.burn1.states:r', value=burn1.interpolate(ys=[1, 1.5],
                                                         nodes='state_input'))
p.set_val('traj.burn1.states:theta', value=burn1.interpolate(ys=[0, 1.7],
                                                             nodes='state_input'))
p.set_val('traj.burn1.states:vr', value=burn1.interpolate(ys=[0, 0],
                                                          nodes='state_input'))
p.set_val('traj.burn1.states:vt', value=burn1.interpolate(ys=[1, 1],
                                                          nodes='state_input'))
p.set_val('traj.burn1.states:accel', value=burn1.interpolate(ys=[0.1, 0],
                                                             nodes='state_input'))
p.set_val('traj.burn1.states:deltav', value=burn1.interpolate(ys=[0, 0.1],
                                                              nodes='state_input'))
p.set_val('traj.burn1.controls:u1',
          value=burn1.interpolate(ys=[-3.5, 13.0], nodes='control_input'))

p.set_val('traj.coast.t_initial', value=2.25)
p.set_val('traj.coast.t_duration', value=3.0)

p.set_val('traj.coast.states:r', value=coast.interpolate(ys=[1.3, 1.5],
                                                         nodes='state_input'))
p.set_val('traj.coast.states:theta',
          value=coast.interpolate(ys=[2.1767, 1.7], nodes='state_input'))

p.set_val('traj.coast.states:vr', value=coast.interpolate(ys=[0.3285, 0],
                                                          nodes='state_input'))
p.set_val('traj.coast.states:vt', value=coast.interpolate(ys=[0.97, 1],
                                                          nodes='state_input'))
p.set_val('traj.coast.states:accel', value=coast.interpolate(ys=[0, 0],
                                                             nodes='state_input'))

p.set_val('traj.burn2.t_initial', value=5.25)
p.set_val('traj.burn2.t_duration', value=1.75)

p.set_val('traj.burn2.states:r', value=burn2.interpolate(ys=[1, 3.],
                                                         nodes='state_input'))
p.set_val('traj.burn2.states:theta', value=burn2.interpolate(ys=[0, 4.0],
                                                             nodes='state_input'))
p.set_val('traj.burn2.states:vr', value=burn2.interpolate(ys=[0, 0],
                                                          nodes='state_input'))
p.set_val('traj.burn2.states:vt',
          value=burn2.interpolate(ys=[1, np.sqrt(1 / 3.)],
                                  nodes='state_input'))
p.set_val('traj.burn2.states:deltav',
          value=burn2.interpolate(ys=[0.1, 0.2], nodes='state_input'))
p.set_val('traj.burn2.states:accel', value=burn2.interpolate(ys=[0.1, 0],
                                                             nodes='state_input'))

p.set_val('traj.burn2.controls:u1', value=burn2.interpolate(ys=[0, 0],
                                                            nodes='control_input'))

dm.run_problem(p)



#
# Plot results
#
traj = p.model.traj
exp_out = traj.simulate()

fig = plt.figure(figsize=(8, 4))
fig.suptitle('Two Burn Orbit Raise Solution')
ax_u1 = plt.subplot2grid((2, 2), (0, 0))
ax_deltav = plt.subplot2grid((2, 2), (1, 0))
ax_xy = plt.subplot2grid((2, 2), (0, 1), rowspan=2)

span = np.linspace(0, 2 * np.pi, 100)
ax_xy.plot(np.cos(span), np.sin(span), 'k--', lw=1)
ax_xy.plot(3 * np.cos(span), 3 * np.sin(span), 'k--', lw=1)
ax_xy.set_xlim(-4.5, 4.5)
ax_xy.set_ylim(-4.5, 4.5)

ax_xy.set_xlabel('x ($R_e$)')
ax_xy.set_ylabel('y ($R_e$)')

ax_u1.set_xlabel('time ($TU$)')
ax_u1.set_ylabel('$u_1$ ($deg$)')
ax_u1.grid(True)

ax_deltav.set_xlabel('time ($TU$)')
ax_deltav.set_ylabel('${\Delta}v$ ($DU/TU$)')
ax_deltav.grid(True)

t_sol = dict((phs, p.get_val('traj.{0}.timeseries.time'.format(phs)))
             for phs in ['burn1', 'coast', 'burn2'])
x_sol = dict((phs, p.get_val('traj.{0}.timeseries.pos_x'.format(phs)))
             for phs in ['burn1', 'coast', 'burn2'])
y_sol = dict((phs, p.get_val('traj.{0}.timeseries.pos_y'.format(phs)))
             for phs in ['burn1', 'coast', 'burn2'])
dv_sol = dict((phs, p.get_val('traj.{0}.timeseries.states:deltav'.format(phs)))
              for phs in ['burn1', 'coast', 'burn2'])
u1_sol = dict((phs, p.get_val('traj.{0}.timeseries.controls:u1'.format(phs), units='deg'))
              for phs in ['burn1', 'burn2'])

t_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.time'.format(phs)))
             for phs in ['burn1', 'coast', 'burn2'])
x_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.pos_x'.format(phs)))
             for phs in ['burn1', 'coast', 'burn2'])
y_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.pos_y'.format(phs)))
             for phs in ['burn1', 'coast', 'burn2'])
dv_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.states:deltav'.format(phs)))
              for phs in ['burn1', 'coast', 'burn2'])
u1_exp = dict((phs, exp_out.get_val('traj.{0}.timeseries.controls:u1'.format(phs),
                                    units='deg'))
              for phs in ['burn1', 'burn2'])

for phs in ['burn1', 'coast', 'burn2']:
    try:
        ax_u1.plot(t_exp[phs], u1_exp[phs], '-', marker=None, color='C0')
        ax_u1.plot(t_sol[phs], u1_sol[phs], 'o', mfc='C1', mec='C1', ms=3)
    except KeyError:
        pass

    ax_deltav.plot(t_exp[phs], dv_exp[phs], '-', marker=None, color='C0')
    ax_deltav.plot(t_sol[phs], dv_sol[phs], 'o', mfc='C1', mec='C1', ms=3)

    ax_xy.plot(x_exp[phs], y_exp[phs], '-', marker=None, color='C0', label='explicit')
    ax_xy.plot(x_sol[phs], y_sol[phs], 'o', mfc='C1', mec='C1', ms=3, label='implicit')

plt.show()
--- Linkage Report [traj] ---
    --- burn1 - coast ---
        time   [final]  ==  time   [initial]
        r      [final]  ==  r      [initial]
        theta  [final]  ==  theta  [initial]
        vr     [final]  ==  vr     [initial]
        vt     [final]  ==  vt     [initial]
        deltav [final]  ==  deltav [initial]
----------------------------
    --- coast - burn2 ---
        time   [final]  ==  time   [initial]
        r      [final]  ==  r      [initial]
        theta  [final]  ==  theta  [initial]
        vr     [final]  ==  vr     [initial]
        vt     [final]  ==  vt     [initial]
        deltav [final]  ==  deltav [initial]
----------------------------
    --- burn1 - burn2 ---
        accel [final]  ==  accel [initial]
----------------------------
/home/travis/build/OpenMDAO/dymos/OpenMDAO/openmdao/core/problem.py:969: RuntimeWarning:Inefficient choice of derivative mode.  You chose 'fwd' for a problem with 215 design variables and 129 response variables (objectives and nonlinear constraints).
/home/travis/build/OpenMDAO/dymos/OpenMDAO/openmdao/core/problem.py:969: RuntimeWarning:Inefficient choice of derivative mode.  You chose 'fwd' for a problem with 215 design variables and 129 response variables (objectives and nonlinear constraints).
INFO: checking out_of_order
INFO: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
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
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
Full total jacobian was computed 3 times, taking 0.763499 seconds.
Total jacobian shape: (120, 204) 


Jacobian shape: (120, 204)  ( 4.92% nonzero)
FWD solves: 19   REV solves: 0
Total colors vs. total size: 19 vs 204  (90.7% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.763499 sec.
Time to compute coloring: 0.006730 sec.


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

    Solution: 
--------------------------------------------------------------------------------
    Total Time:                    2.4732
       User Objective Time :       0.3494
       User Sensitivity Time :     1.1510
       Interface Time :            0.8689
       Opt Solver Time:            0.1039
    Calls to Objective Function :      22
    Calls to Sens Function :           22


   Objectives
      Index  Name                                                    Value          Optimum
          0  traj.phases.burn2.indep_states.states:deltav     3.989866E+01     0.000000E+00

   Variables (c - continuous, i - integer, d - discrete)
      Index  Name                                                            Type      Lower Bound            Value      Upper Bound     Status
          0  traj.phases.burn1.time_extents.t_duration_0                        c     5.000000E-01     2.228067E+00     1.000000E+01           
          1  traj.phases.burn1.indep_states.states:r_0                          c    -1.000000E+21     1.002362E+00     1.000000E+21           
          2  traj.phases.burn1.indep_states.states:r_1                          c    -1.000000E+21     1.002362E+00     1.000000E+21           
          3  traj.phases.burn1.indep_states.states:r_2                          c    -1.000000E+21     1.021638E+00     1.000000E+21           
          4  traj.phases.burn1.indep_states.states:r_3                          c    -1.000000E+21     1.021638E+00     1.000000E+21           
          5  traj.phases.burn1.indep_states.states:r_4                          c    -1.000000E+21     1.072722E+00     1.000000E+21           
          6  traj.phases.burn1.indep_states.states:r_5                          c    -1.000000E+21     1.072722E+00     1.000000E+21           
          7  traj.phases.burn1.indep_states.states:r_6                          c    -1.000000E+21     1.162491E+00     1.000000E+21           
          8  traj.phases.burn1.indep_states.states:r_7                          c    -1.000000E+21     1.162491E+00     1.000000E+21           
          9  traj.phases.burn1.indep_states.states:r_8                          c    -1.000000E+21     1.289884E+00     1.000000E+21           
         10  traj.phases.burn1.indep_states.states:theta_0                      c    -1.000000E+21     4.551388E-01     1.000000E+21           
         11  traj.phases.burn1.indep_states.states:theta_1                      c    -1.000000E+21     4.551388E-01     1.000000E+21           
         12  traj.phases.burn1.indep_states.states:theta_2                      c    -1.000000E+21     9.220014E-01     1.000000E+21           
         13  traj.phases.burn1.indep_states.states:theta_3                      c    -1.000000E+21     9.220014E-01     1.000000E+21           
         14  traj.phases.burn1.indep_states.states:theta_4                      c    -1.000000E+21     1.378708E+00     1.000000E+21           
         15  traj.phases.burn1.indep_states.states:theta_5                      c    -1.000000E+21     1.378708E+00     1.000000E+21           
         16  traj.phases.burn1.indep_states.states:theta_6                      c    -1.000000E+21     1.798798E+00     1.000000E+21           
         17  traj.phases.burn1.indep_states.states:theta_7                      c    -1.000000E+21     1.798798E+00     1.000000E+21           
         18  traj.phases.burn1.indep_states.states:theta_8                      c    -1.000000E+21     2.165079E+00     1.000000E+21           
         19  traj.phases.burn1.indep_states.states:vr_0                         c    -1.000000E+21     1.761706E-02     1.000000E+21           
         20  traj.phases.burn1.indep_states.states:vr_1                         c    -1.000000E+21     1.761706E-02     1.000000E+21           
         21  traj.phases.burn1.indep_states.states:vr_2                         c    -1.000000E+21     7.464416E-02     1.000000E+21           
         22  traj.phases.burn1.indep_states.states:vr_3                         c    -1.000000E+21     7.464416E-02     1.000000E+21           
         23  traj.phases.burn1.indep_states.states:vr_4                         c    -1.000000E+21     1.571939E-01     1.000000E+21           
         24  traj.phases.burn1.indep_states.states:vr_5                         c    -1.000000E+21     1.571939E-01     1.000000E+21           
         25  traj.phases.burn1.indep_states.states:vr_6                         c    -1.000000E+21     2.451474E-01     1.000000E+21           
         26  traj.phases.burn1.indep_states.states:vr_7                         c    -1.000000E+21     2.451474E-01     1.000000E+21           
         27  traj.phases.burn1.indep_states.states:vr_8                         c    -1.000000E+21     3.246997E-01     1.000000E+21           
         28  traj.phases.burn1.indep_states.states:vt_0                         c    -1.000000E+21     1.042729E+00     1.000000E+21           
         29  traj.phases.burn1.indep_states.states:vt_1                         c    -1.000000E+21     1.042729E+00     1.000000E+21           
         30  traj.phases.burn1.indep_states.states:vt_2                         c    -1.000000E+21     1.069160E+00     1.000000E+21           
         31  traj.phases.burn1.indep_states.states:vt_3                         c    -1.000000E+21     1.069160E+00     1.000000E+21           
         32  traj.phases.burn1.indep_states.states:vt_4                         c    -1.000000E+21     1.065015E+00     1.000000E+21           
         33  traj.phases.burn1.indep_states.states:vt_5                         c    -1.000000E+21     1.065015E+00     1.000000E+21           
         34  traj.phases.burn1.indep_states.states:vt_6                         c    -1.000000E+21     1.030065E+00     1.000000E+21           
         35  traj.phases.burn1.indep_states.states:vt_7                         c    -1.000000E+21     1.030065E+00     1.000000E+21           
         36  traj.phases.burn1.indep_states.states:vt_8                         c    -1.000000E+21     9.761566E-01     1.000000E+21           
         37  traj.phases.burn1.indep_states.states:accel_0                      c    -1.000000E+21     1.030617E-01     1.000000E+21           
         38  traj.phases.burn1.indep_states.states:accel_1                      c    -1.000000E+21     1.030617E-01     1.000000E+21           
         39  traj.phases.burn1.indep_states.states:accel_2                      c    -1.000000E+21     1.063168E-01     1.000000E+21           
         40  traj.phases.burn1.indep_states.states:accel_3                      c    -1.000000E+21     1.063168E-01     1.000000E+21           
         41  traj.phases.burn1.indep_states.states:accel_4                      c    -1.000000E+21     1.097843E-01     1.000000E+21           
         42  traj.phases.burn1.indep_states.states:accel_5                      c    -1.000000E+21     1.097843E-01     1.000000E+21           
         43  traj.phases.burn1.indep_states.states:accel_6                      c    -1.000000E+21     1.134855E-01     1.000000E+21           
         44  traj.phases.burn1.indep_states.states:accel_7                      c    -1.000000E+21     1.134855E-01     1.000000E+21           
         45  traj.phases.burn1.indep_states.states:accel_8                      c    -1.000000E+21     1.174450E-01     1.000000E+21           
         46  traj.phases.burn1.indep_states.states:deltav_0                     c    -1.000000E+21     4.523666E-02     1.000000E+21           
         47  traj.phases.burn1.indep_states.states:deltav_1                     c    -1.000000E+21     4.523666E-02     1.000000E+21           
         48  traj.phases.burn1.indep_states.states:deltav_2                     c    -1.000000E+21     9.188009E-02     1.000000E+21           
         49  traj.phases.burn1.indep_states.states:deltav_3                     c    -1.000000E+21     9.188009E-02     1.000000E+21           
         50  traj.phases.burn1.indep_states.states:deltav_4                     c    -1.000000E+21     1.400206E-01     1.000000E+21           
         51  traj.phases.burn1.indep_states.states:deltav_5                     c    -1.000000E+21     1.400206E-01     1.000000E+21           
         52  traj.phases.burn1.indep_states.states:deltav_6                     c    -1.000000E+21     1.897575E-01     1.000000E+21           
         53  traj.phases.burn1.indep_states.states:deltav_7                     c    -1.000000E+21     1.897575E-01     1.000000E+21           
         54  traj.phases.burn1.indep_states.states:deltav_8                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
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         56  traj.phases.burn1.control_group.indep_controls.controls:u1_1       c    -3.000000E-01    -3.085405E-02     3.000000E-01           
         57  traj.phases.burn1.control_group.indep_controls.controls:u1_2       c    -3.000000E-01    -1.574136E-02     3.000000E-01           
         58  traj.phases.burn1.control_group.indep_controls.controls:u1_3       c    -3.000000E-01    -1.574136E-02     3.000000E-01           
         59  traj.phases.burn1.control_group.indep_controls.controls:u1_4       c    -3.000000E-01     2.033705E-04     3.000000E-01           
         60  traj.phases.burn1.control_group.indep_controls.controls:u1_5       c    -3.000000E-01     1.698016E-02     3.000000E-01           
         61  traj.phases.burn1.control_group.indep_controls.controls:u1_6       c    -3.000000E-01     1.698016E-02     3.000000E-01           
         62  traj.phases.burn1.control_group.indep_controls.controls:u1_7       c    -3.000000E-01     3.458900E-02     3.000000E-01           
         63  traj.phases.burn1.control_group.indep_controls.controls:u1_8       c    -3.000000E-01     5.302990E-02     3.000000E-01           
         64  traj.phases.burn1.control_group.indep_controls.controls:u1_9       c    -3.000000E-01     5.302990E-02     3.000000E-01           
         65  traj.phases.burn1.control_group.indep_controls.controls:u1_10      c    -3.000000E-01     7.230284E-02     3.000000E-01           
         66  traj.phases.burn1.control_group.indep_controls.controls:u1_11      c    -3.000000E-01     9.240785E-02     3.000000E-01           
         67  traj.phases.burn1.control_group.indep_controls.controls:u1_12      c    -3.000000E-01     9.240785E-02     3.000000E-01           
         68  traj.phases.burn1.control_group.indep_controls.controls:u1_13      c    -3.000000E-01     1.133449E-01     3.000000E-01           
         69  traj.phases.burn1.control_group.indep_controls.controls:u1_14      c    -3.000000E-01     1.351140E-01     3.000000E-01           
         70  traj.phases.coast.time_extents.t_initial_0                         c     5.000000E-01     2.228067E+00     2.000000E+01           
         71  traj.phases.coast.time_extents.t_duration_0                        c     1.000000E-02     1.477294E-01     1.000000E+00           
         72  traj.phases.coast.indep_states.states:r_0                          c    -1.000000E+21     1.289884E+00     1.000000E+21           
         73  traj.phases.coast.indep_states.states:r_1                          c    -1.000000E+21     1.826977E+00     1.000000E+21           
         74  traj.phases.coast.indep_states.states:r_2                          c    -1.000000E+21     1.826977E+00     1.000000E+21           
         75  traj.phases.coast.indep_states.states:r_3                          c    -1.000000E+21     2.302612E+00     1.000000E+21           
         76  traj.phases.coast.indep_states.states:r_4                          c    -1.000000E+21     2.302612E+00     1.000000E+21           
         77  traj.phases.coast.indep_states.states:r_5                          c    -1.000000E+21     2.652893E+00     1.000000E+21           
         78  traj.phases.coast.indep_states.states:r_6                          c    -1.000000E+21     2.652893E+00     1.000000E+21           
         79  traj.phases.coast.indep_states.states:r_7                          c    -1.000000E+21     2.878555E+00     1.000000E+21           
         80  traj.phases.coast.indep_states.states:r_8                          c    -1.000000E+21     2.878555E+00     1.000000E+21           
         81  traj.phases.coast.indep_states.states:r_9                          c    -1.000000E+21     2.985662E+00     1.000000E+21           
         82  traj.phases.coast.indep_states.states:theta_0                      c    -1.000000E+21     2.165079E+00     1.000000E+21           
         83  traj.phases.coast.indep_states.states:theta_1                      c    -1.000000E+21     2.959758E+00     1.000000E+21           
         84  traj.phases.coast.indep_states.states:theta_2                      c    -1.000000E+21     2.959758E+00     1.000000E+21           
         85  traj.phases.coast.indep_states.states:theta_3                      c    -1.000000E+21     3.397889E+00     1.000000E+21           
         86  traj.phases.coast.indep_states.states:theta_4                      c    -1.000000E+21     3.397889E+00     1.000000E+21           
         87  traj.phases.coast.indep_states.states:theta_5                      c    -1.000000E+21     3.699840E+00     1.000000E+21           
         88  traj.phases.coast.indep_states.states:theta_6                      c    -1.000000E+21     3.699840E+00     1.000000E+21           
         89  traj.phases.coast.indep_states.states:theta_7                      c    -1.000000E+21     3.941679E+00     1.000000E+21           
         90  traj.phases.coast.indep_states.states:theta_8                      c    -1.000000E+21     3.941679E+00     1.000000E+21           
         91  traj.phases.coast.indep_states.states:theta_9                      c    -1.000000E+21     4.156717E+00     1.000000E+21           
         92  traj.phases.coast.indep_states.states:vr_0                         c    -1.000000E+21     3.246997E-01     1.000000E+21           
         93  traj.phases.coast.indep_states.states:vr_1                         c    -1.000000E+21     3.587944E-01     1.000000E+21           
         94  traj.phases.coast.indep_states.states:vr_2                         c    -1.000000E+21     3.587944E-01     1.000000E+21           
         95  traj.phases.coast.indep_states.states:vr_3                         c    -1.000000E+21     2.804105E-01     1.000000E+21           
         96  traj.phases.coast.indep_states.states:vr_4                         c    -1.000000E+21     2.804105E-01     1.000000E+21           
         97  traj.phases.coast.indep_states.states:vr_5                         c    -1.000000E+21     1.941935E-01     1.000000E+21           
         98  traj.phases.coast.indep_states.states:vr_6                         c    -1.000000E+21     1.941935E-01     1.000000E+21           
         99  traj.phases.coast.indep_states.states:vr_7                         c    -1.000000E+21     1.120402E-01     1.000000E+21           
        100  traj.phases.coast.indep_states.states:vr_8                         c    -1.000000E+21     1.120402E-01     1.000000E+21           
        101  traj.phases.coast.indep_states.states:vr_9                         c    -1.000000E+21     3.335887E-02     1.000000E+21           
        102  traj.phases.coast.indep_states.states:vt_0                         c    -1.000000E+21     9.761566E-01     1.000000E+21           
        103  traj.phases.coast.indep_states.states:vt_1                         c    -1.000000E+21     6.893007E-01     1.000000E+21           
        104  traj.phases.coast.indep_states.states:vt_2                         c    -1.000000E+21     6.893007E-01     1.000000E+21           
        105  traj.phases.coast.indep_states.states:vt_3                         c    -1.000000E+21     5.469088E-01     1.000000E+21           
        106  traj.phases.coast.indep_states.states:vt_4                         c    -1.000000E+21     5.469088E-01     1.000000E+21           
        107  traj.phases.coast.indep_states.states:vt_5                         c    -1.000000E+21     4.746907E-01     1.000000E+21           
        108  traj.phases.coast.indep_states.states:vt_6                         c    -1.000000E+21     4.746907E-01     1.000000E+21           
        109  traj.phases.coast.indep_states.states:vt_7                         c    -1.000000E+21     4.374758E-01     1.000000E+21           
        110  traj.phases.coast.indep_states.states:vt_8                         c    -1.000000E+21     4.374758E-01     1.000000E+21           
        111  traj.phases.coast.indep_states.states:vt_9                         c    -1.000000E+21     4.217812E-01     1.000000E+21           
        112  traj.phases.coast.indep_states.states:accel_0                      c    -1.000000E+21    -7.487132E-35     1.000000E+21           
        113  traj.phases.coast.indep_states.states:accel_1                      c    -1.000000E+21    -1.882633E-36     1.000000E+21           
        114  traj.phases.coast.indep_states.states:accel_2                      c    -1.000000E+21    -1.872348E-36     1.000000E+21           
        115  traj.phases.coast.indep_states.states:accel_3                      c    -1.000000E+21    -2.978598E-34     1.000000E+21           
        116  traj.phases.coast.indep_states.states:accel_4                      c    -1.000000E+21     1.298623E-34     1.000000E+21           
        117  traj.phases.coast.indep_states.states:accel_5                      c    -1.000000E+21    -1.250994E-34     1.000000E+21           
        118  traj.phases.coast.indep_states.states:accel_6                      c    -1.000000E+21    -1.250641E-34     1.000000E+21           
        119  traj.phases.coast.indep_states.states:accel_7                      c    -1.000000E+21    -3.320528E-34     1.000000E+21           
        120  traj.phases.coast.indep_states.states:deltav_0                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
        121  traj.phases.coast.indep_states.states:deltav_1                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
        122  traj.phases.coast.indep_states.states:deltav_2                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
        123  traj.phases.coast.indep_states.states:deltav_3                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
        124  traj.phases.coast.indep_states.states:deltav_4                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
        125  traj.phases.coast.indep_states.states:deltav_5                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
        126  traj.phases.coast.indep_states.states:deltav_6                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
        127  traj.phases.coast.indep_states.states:deltav_7                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
        128  traj.phases.coast.indep_states.states:deltav_8                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
        129  traj.phases.coast.indep_states.states:deltav_9                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
        130  traj.phases.burn2.time_extents.t_initial_0                         c     5.000000E-02     9.614537E-01     5.000000E+00           
        131  traj.phases.burn2.time_extents.t_duration_0                        c     5.000000E-01     1.275243E+00     1.000000E+01           
        132  traj.phases.burn2.indep_states.states:r_0                          c    -1.000000E+21     2.985662E+00     1.000000E+21           
        133  traj.phases.burn2.indep_states.states:r_1                          c    -1.000000E+21     2.992648E+00     1.000000E+21           
        134  traj.phases.burn2.indep_states.states:r_2                          c    -1.000000E+21     2.992648E+00     1.000000E+21           
        135  traj.phases.burn2.indep_states.states:r_3                          c    -1.000000E+21     2.996948E+00     1.000000E+21           
        136  traj.phases.burn2.indep_states.states:r_4                          c    -1.000000E+21     2.996948E+00     1.000000E+21           
        137  traj.phases.burn2.indep_states.states:r_5                          c    -1.000000E+21     2.999153E+00     1.000000E+21           
        138  traj.phases.burn2.indep_states.states:r_6                          c    -1.000000E+21     2.999153E+00     1.000000E+21           
        139  traj.phases.burn2.indep_states.states:r_7                          c    -1.000000E+21     2.999922E+00     1.000000E+21           
        140  traj.phases.burn2.indep_states.states:r_8                          c    -1.000000E+21     2.999922E+00     1.000000E+21           
        141  traj.phases.burn2.indep_states.states:theta_0                      c    -1.000000E+21     4.156717E+00     1.000000E+21           
        142  traj.phases.burn2.indep_states.states:theta_1                      c    -1.000000E+21     4.193942E+00     1.000000E+21           
        143  traj.phases.burn2.indep_states.states:theta_2                      c    -1.000000E+21     4.193942E+00     1.000000E+21           
        144  traj.phases.burn2.indep_states.states:theta_3                      c    -1.000000E+21     4.233629E+00     1.000000E+21           
        145  traj.phases.burn2.indep_states.states:theta_4                      c    -1.000000E+21     4.233629E+00     1.000000E+21           
        146  traj.phases.burn2.indep_states.states:theta_5                      c    -1.000000E+21     4.275883E+00     1.000000E+21           
        147  traj.phases.burn2.indep_states.states:theta_6                      c    -1.000000E+21     4.275883E+00     1.000000E+21           
        148  traj.phases.burn2.indep_states.states:theta_7                      c    -1.000000E+21     4.320807E+00     1.000000E+21           
        149  traj.phases.burn2.indep_states.states:theta_8                      c    -1.000000E+21     4.320807E+00     1.000000E+21           
        150  traj.phases.burn2.indep_states.states:theta_9                      c    -1.000000E+21     4.368488E+00     1.000000E+21           
        151  traj.phases.burn2.indep_states.states:vr_0                         c    -1.000000E+21     3.335887E-02     1.000000E+21           
        152  traj.phases.burn2.indep_states.states:vr_1                         c    -1.000000E+21     2.176290E-02     1.000000E+21           
        153  traj.phases.burn2.indep_states.states:vr_2                         c    -1.000000E+21     2.176290E-02     1.000000E+21           
        154  traj.phases.burn2.indep_states.states:vr_3                         c    -1.000000E+21     1.234388E-02     1.000000E+21           
        155  traj.phases.burn2.indep_states.states:vr_4                         c    -1.000000E+21     1.234388E-02     1.000000E+21           
        156  traj.phases.burn2.indep_states.states:vr_5                         c    -1.000000E+21     5.372568E-03     1.000000E+21           
        157  traj.phases.burn2.indep_states.states:vr_6                         c    -1.000000E+21     5.372568E-03     1.000000E+21           
        158  traj.phases.burn2.indep_states.states:vr_7                         c    -1.000000E+21     1.149201E-03     1.000000E+21           
        159  traj.phases.burn2.indep_states.states:vr_8                         c    -1.000000E+21     1.149201E-03     1.000000E+21           
        160  traj.phases.burn2.indep_states.states:vt_0                         c    -1.000000E+21     4.217812E-01     1.000000E+21           
        161  traj.phases.burn2.indep_states.states:vt_1                         c    -1.000000E+21     4.510131E-01     1.000000E+21           
        162  traj.phases.burn2.indep_states.states:vt_2                         c    -1.000000E+21     4.510131E-01     1.000000E+21           
        163  traj.phases.burn2.indep_states.states:vt_3                         c    -1.000000E+21     4.812219E-01     1.000000E+21           
        164  traj.phases.burn2.indep_states.states:vt_4                         c    -1.000000E+21     4.812219E-01     1.000000E+21           
        165  traj.phases.burn2.indep_states.states:vt_5                         c    -1.000000E+21     5.123850E-01     1.000000E+21           
        166  traj.phases.burn2.indep_states.states:vt_6                         c    -1.000000E+21     5.123850E-01     1.000000E+21           
        167  traj.phases.burn2.indep_states.states:vt_7                         c    -1.000000E+21     5.444544E-01     1.000000E+21           
        168  traj.phases.burn2.indep_states.states:vt_8                         c    -1.000000E+21     5.444544E-01     1.000000E+21           
        169  traj.phases.burn2.indep_states.states:accel_0                      c    -1.000000E+21     1.174450E-01     1.000000E+21           
        170  traj.phases.burn2.indep_states.states:accel_1                      c    -1.000000E+21     1.198381E-01     1.000000E+21           
        171  traj.phases.burn2.indep_states.states:accel_2                      c    -1.000000E+21     1.198381E-01     1.000000E+21           
        172  traj.phases.burn2.indep_states.states:accel_3                      c    -1.000000E+21     1.223308E-01     1.000000E+21           
        173  traj.phases.burn2.indep_states.states:accel_4                      c    -1.000000E+21     1.223308E-01     1.000000E+21           
        174  traj.phases.burn2.indep_states.states:accel_5                      c    -1.000000E+21     1.249293E-01     1.000000E+21           
        175  traj.phases.burn2.indep_states.states:accel_6                      c    -1.000000E+21     1.249293E-01     1.000000E+21           
        176  traj.phases.burn2.indep_states.states:accel_7                      c    -1.000000E+21     1.276407E-01     1.000000E+21           
        177  traj.phases.burn2.indep_states.states:accel_8                      c    -1.000000E+21     1.276407E-01     1.000000E+21           
        178  traj.phases.burn2.indep_states.states:accel_9                      c    -1.000000E+21     1.304723E-01     1.000000E+21           
        179  traj.phases.burn2.indep_states.states:deltav_0                     c    -1.000000E+21     2.412003E-01     1.000000E+21           
        180  traj.phases.burn2.indep_states.states:deltav_1                     c    -1.000000E+21     2.714576E-01     1.000000E+21           
        181  traj.phases.burn2.indep_states.states:deltav_2                     c    -1.000000E+21     2.714576E-01     1.000000E+21           
        182  traj.phases.burn2.indep_states.states:deltav_3                     c    -1.000000E+21     3.023379E-01     1.000000E+21           
        183  traj.phases.burn2.indep_states.states:deltav_4                     c    -1.000000E+21     3.023379E-01     1.000000E+21           
        184  traj.phases.burn2.indep_states.states:deltav_5                     c    -1.000000E+21     3.338672E-01     1.000000E+21           
        185  traj.phases.burn2.indep_states.states:deltav_6                     c    -1.000000E+21     3.338672E-01     1.000000E+21           
        186  traj.phases.burn2.indep_states.states:deltav_7                     c    -1.000000E+21     3.660736E-01     1.000000E+21           
        187  traj.phases.burn2.indep_states.states:deltav_8                     c    -1.000000E+21     3.660736E-01     1.000000E+21           
        188  traj.phases.burn2.indep_states.states:deltav_9                     c    -1.000000E+21     3.989866E-01     1.000000E+21           
        189  traj.phases.burn2.control_group.indep_controls.controls:u1_0       c    -9.000000E-01     1.554560E-02     9.000000E-01           
        190  traj.phases.burn2.control_group.indep_controls.controls:u1_1       c    -9.000000E-01     1.313254E-02     9.000000E-01           
        191  traj.phases.burn2.control_group.indep_controls.controls:u1_2       c    -9.000000E-01     1.110237E-02     9.000000E-01           
        192  traj.phases.burn2.control_group.indep_controls.controls:u1_3       c    -9.000000E-01     1.110237E-02     9.000000E-01           
        193  traj.phases.burn2.control_group.indep_controls.controls:u1_4       c    -9.000000E-01     9.455084E-03     9.000000E-01           
        194  traj.phases.burn2.control_group.indep_controls.controls:u1_5       c    -9.000000E-01     8.190691E-03     9.000000E-01           
        195  traj.phases.burn2.control_group.indep_controls.controls:u1_6       c    -9.000000E-01     8.190691E-03     9.000000E-01           
        196  traj.phases.burn2.control_group.indep_controls.controls:u1_7       c    -9.000000E-01     7.309186E-03     9.000000E-01           
        197  traj.phases.burn2.control_group.indep_controls.controls:u1_8       c    -9.000000E-01     6.810569E-03     9.000000E-01           
        198  traj.phases.burn2.control_group.indep_controls.controls:u1_9       c    -9.000000E-01     6.810569E-03     9.000000E-01           
        199  traj.phases.burn2.control_group.indep_controls.controls:u1_10      c    -9.000000E-01     6.694842E-03     9.000000E-01           
        200  traj.phases.burn2.control_group.indep_controls.controls:u1_11      c    -9.000000E-01     6.962004E-03     9.000000E-01           
        201  traj.phases.burn2.control_group.indep_controls.controls:u1_12      c    -9.000000E-01     6.962004E-03     9.000000E-01           
        202  traj.phases.burn2.control_group.indep_controls.controls:u1_13      c    -9.000000E-01     7.612054E-03     9.000000E-01           
        203  traj.phases.burn2.control_group.indep_controls.controls:u1_14      c    -9.000000E-01     8.644993E-03     9.000000E-01           

   Constraints (i - inequality, e - equality)
      Index  Name                                                            Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
          0  traj.phases.burn1.collocation_constraint.defects:r                 e   0.000000E+00   -1.913215E-15    0.000000E+00              9.00000E+100
          1  traj.phases.burn1.collocation_constraint.defects:r                 e   0.000000E+00   -4.947303E-15    0.000000E+00              9.00000E+100
          2  traj.phases.burn1.collocation_constraint.defects:r                 e   0.000000E+00    6.184129E-15    0.000000E+00              9.00000E+100
          3  traj.phases.burn1.collocation_constraint.defects:r                 e   0.000000E+00    2.473652E-15    0.000000E+00              9.00000E+100
          4  traj.phases.burn1.collocation_constraint.defects:r                 e   0.000000E+00    1.236826E-15    0.000000E+00              9.00000E+100
          5  traj.phases.burn1.collocation_constraint.defects:theta             e   0.000000E+00   -4.947303E-15    0.000000E+00              9.00000E+100
          6  traj.phases.burn1.collocation_constraint.defects:theta             e   0.000000E+00    9.894607E-15    0.000000E+00              9.00000E+100
          7  traj.phases.burn1.collocation_constraint.defects:theta             e   0.000000E+00   -9.894607E-15    0.000000E+00              9.00000E+100
          8  traj.phases.burn1.collocation_constraint.defects:theta             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
          9  traj.phases.burn1.collocation_constraint.defects:theta             e   0.000000E+00   -4.947303E-15    0.000000E+00              9.00000E+100
         10  traj.phases.burn1.collocation_constraint.defects:vr                e   0.000000E+00   -1.174985E-14    0.000000E+00              9.00000E+100
         11  traj.phases.burn1.collocation_constraint.defects:vr                e   0.000000E+00    1.978921E-14    0.000000E+00              9.00000E+100
         12  traj.phases.burn1.collocation_constraint.defects:vr                e   0.000000E+00    6.184129E-16    0.000000E+00              9.00000E+100
         13  traj.phases.burn1.collocation_constraint.defects:vr                e   0.000000E+00    6.184129E-16    0.000000E+00              9.00000E+100
         14  traj.phases.burn1.collocation_constraint.defects:vr                e   0.000000E+00    6.184129E-15    0.000000E+00              9.00000E+100
         15  traj.phases.burn1.collocation_constraint.defects:vt                e   0.000000E+00    1.546032E-15    0.000000E+00              9.00000E+100
         16  traj.phases.burn1.collocation_constraint.defects:vt                e   0.000000E+00   -1.113143E-14    0.000000E+00              9.00000E+100
         17  traj.phases.burn1.collocation_constraint.defects:vt                e   0.000000E+00    1.658120E-14    0.000000E+00              9.00000E+100
         18  traj.phases.burn1.collocation_constraint.defects:vt                e   0.000000E+00   -3.710478E-15    0.000000E+00              9.00000E+100
         19  traj.phases.burn1.collocation_constraint.defects:vt                e   0.000000E+00   -2.782858E-15    0.000000E+00              9.00000E+100
         20  traj.phases.burn1.collocation_constraint.defects:accel             e   0.000000E+00   -1.739286E-18    0.000000E+00              9.00000E+100
         21  traj.phases.burn1.collocation_constraint.defects:accel             e   0.000000E+00    6.957145E-18    0.000000E+00              9.00000E+100
         22  traj.phases.burn1.collocation_constraint.defects:accel             e   0.000000E+00   -2.898811E-18    0.000000E+00              9.00000E+100
         23  traj.phases.burn1.collocation_constraint.defects:accel             e   0.000000E+00    1.004921E-17    0.000000E+00              9.00000E+100
         24  traj.phases.burn1.collocation_constraint.defects:accel             e   0.000000E+00   -4.638097E-18    0.000000E+00              9.00000E+100
         25  traj.phases.burn1.collocation_constraint.defects:deltav            e   0.000000E+00    9.276194E-18    0.000000E+00              9.00000E+100
         26  traj.phases.burn1.collocation_constraint.defects:deltav            e   0.000000E+00    1.546032E-17    0.000000E+00              9.00000E+100
         27  traj.phases.burn1.collocation_constraint.defects:deltav            e   0.000000E+00   -6.184129E-18    0.000000E+00              9.00000E+100
         28  traj.phases.burn1.collocation_constraint.defects:deltav            e   0.000000E+00    6.184129E-18    0.000000E+00              9.00000E+100
         29  traj.phases.burn1.collocation_constraint.defects:deltav            e   0.000000E+00    2.782858E-17    0.000000E+00              9.00000E+100
         30  traj.phases.burn1.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         31  traj.phases.burn1.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         32  traj.phases.burn1.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         33  traj.phases.burn1.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         34  traj.phases.burn1.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         35  traj.phases.burn1.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         36  traj.phases.burn1.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         37  traj.phases.burn1.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         38  traj.phases.burn1.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         39  traj.phases.burn1.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         40  traj.phases.burn1.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         41  traj.phases.burn1.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         42  traj.phases.burn1.continuity_comp.defect_states:vt                 e   0.000000E+00   -2.458274E-20    0.000000E+00              9.00000E+100
         43  traj.phases.burn1.continuity_comp.defect_states:vt                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         44  traj.phases.burn1.continuity_comp.defect_states:vt                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         45  traj.phases.burn1.continuity_comp.defect_states:vt                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         46  traj.phases.burn1.continuity_comp.defect_states:accel              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         47  traj.phases.burn1.continuity_comp.defect_states:accel              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         48  traj.phases.burn1.continuity_comp.defect_states:accel              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         49  traj.phases.burn1.continuity_comp.defect_states:accel              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         50  traj.phases.burn1.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         51  traj.phases.burn1.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         52  traj.phases.burn1.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         53  traj.phases.burn1.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         54  traj.phases.burn1.continuity_comp.defect_controls:u1               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         55  traj.phases.burn1.continuity_comp.defect_controls:u1               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         56  traj.phases.burn1.continuity_comp.defect_controls:u1               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         57  traj.phases.burn1.continuity_comp.defect_controls:u1               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         58  traj.phases.burn1.continuity_comp.defect_control_rates:u1_rate     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         59  traj.phases.burn1.continuity_comp.defect_control_rates:u1_rate     e   0.000000E+00   -1.088407E-17    0.000000E+00              9.00000E+100
         60  traj.phases.burn1.continuity_comp.defect_control_rates:u1_rate     e   0.000000E+00   -9.894607E-18    0.000000E+00              9.00000E+100
         61  traj.phases.burn1.continuity_comp.defect_control_rates:u1_rate     e   0.000000E+00   -7.915685E-18    0.000000E+00              9.00000E+100
         62  traj.phases.burn1.continuity_comp.defect_control_rates:u1_rate2    e   0.000000E+00    2.755731E-17    0.000000E+00              9.00000E+100
         63  traj.phases.burn1.continuity_comp.defect_control_rates:u1_rate2    e   0.000000E+00    2.645502E-17    0.000000E+00              9.00000E+100
         64  traj.phases.burn1.continuity_comp.defect_control_rates:u1_rate2    e   0.000000E+00    2.480158E-18    0.000000E+00              9.00000E+100
         65  traj.phases.burn1.continuity_comp.defect_control_rates:u1_rate2    e   0.000000E+00   -4.436727E-17    0.000000E+00              9.00000E+100
         66  traj.phases.coast.collocation_constraint.defects:r                 e   0.000000E+00    1.640126E-14    0.000000E+00              9.00000E+100
         67  traj.phases.coast.collocation_constraint.defects:r                 e   0.000000E+00   -2.050157E-14    0.000000E+00              9.00000E+100
         68  traj.phases.coast.collocation_constraint.defects:r                 e   0.000000E+00    2.460188E-14    0.000000E+00              9.00000E+100
         69  traj.phases.coast.collocation_constraint.defects:r                 e   0.000000E+00   -1.230094E-14    0.000000E+00              9.00000E+100
         70  traj.phases.coast.collocation_constraint.defects:r                 e   0.000000E+00   -3.280251E-14    0.000000E+00              9.00000E+100
         71  traj.phases.coast.collocation_constraint.defects:theta             e   0.000000E+00    3.280251E-14    0.000000E+00              9.00000E+100
         72  traj.phases.coast.collocation_constraint.defects:theta             e   0.000000E+00   -3.280251E-14    0.000000E+00              9.00000E+100
         73  traj.phases.coast.collocation_constraint.defects:theta             e   0.000000E+00    2.870220E-14    0.000000E+00              9.00000E+100
         74  traj.phases.coast.collocation_constraint.defects:theta             e   0.000000E+00   -2.460188E-14    0.000000E+00              9.00000E+100
         75  traj.phases.coast.collocation_constraint.defects:theta             e   0.000000E+00   -6.150471E-15    0.000000E+00              9.00000E+100
         76  traj.phases.coast.collocation_constraint.defects:vr                e   0.000000E+00   -2.562696E-15    0.000000E+00              9.00000E+100
         77  traj.phases.coast.collocation_constraint.defects:vr                e   0.000000E+00    7.175550E-15    0.000000E+00              9.00000E+100
         78  traj.phases.coast.collocation_constraint.defects:vr                e   0.000000E+00   -5.125393E-15    0.000000E+00              9.00000E+100
         79  traj.phases.coast.collocation_constraint.defects:vr                e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         80  traj.phases.coast.collocation_constraint.defects:vr                e   0.000000E+00   -3.075236E-15    0.000000E+00              9.00000E+100
         81  traj.phases.coast.collocation_constraint.defects:vt                e   0.000000E+00   -6.150471E-15    0.000000E+00              9.00000E+100
         82  traj.phases.coast.collocation_constraint.defects:vt                e   0.000000E+00    3.075236E-15    0.000000E+00              9.00000E+100
         83  traj.phases.coast.collocation_constraint.defects:vt                e   0.000000E+00    3.587775E-15    0.000000E+00              9.00000E+100
         84  traj.phases.coast.collocation_constraint.defects:vt                e   0.000000E+00   -3.331505E-15    0.000000E+00              9.00000E+100
         85  traj.phases.coast.collocation_constraint.defects:vt                e   0.000000E+00   -1.665753E-15    0.000000E+00              9.00000E+100
         86  traj.phases.coast.collocation_constraint.defects:accel             e   0.000000E+00   -5.615349E-35    0.000000E+00              9.00000E+100
         87  traj.phases.coast.collocation_constraint.defects:accel             e   0.000000E+00    7.714182E-39    0.000000E+00              9.00000E+100
         88  traj.phases.coast.collocation_constraint.defects:accel             e   0.000000E+00    3.207915E-34    0.000000E+00              9.00000E+100
         89  traj.phases.coast.collocation_constraint.defects:accel             e   0.000000E+00    2.644862E-38    0.000000E+00              9.00000E+100
         90  traj.phases.coast.collocation_constraint.defects:accel             e   0.000000E+00    2.490396E-34    0.000000E+00              9.00000E+100
         91  traj.phases.coast.collocation_constraint.defects:deltav            e   0.000000E+00    4.147760E-35    0.000000E+00              9.00000E+100
         92  traj.phases.coast.collocation_constraint.defects:deltav            e   0.000000E+00    2.080204E-36    0.000000E+00              9.00000E+100
         93  traj.phases.coast.collocation_constraint.defects:deltav            e   0.000000E+00    9.306811E-35    0.000000E+00              9.00000E+100
         94  traj.phases.coast.collocation_constraint.defects:deltav            e   0.000000E+00    1.385868E-34    0.000000E+00              9.00000E+100
         95  traj.phases.coast.collocation_constraint.defects:deltav            e   0.000000E+00    1.839523E-34    0.000000E+00              9.00000E+100
         96  traj.phases.coast.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         97  traj.phases.coast.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         98  traj.phases.coast.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
         99  traj.phases.coast.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        100  traj.phases.coast.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        101  traj.phases.coast.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        102  traj.phases.coast.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        103  traj.phases.coast.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        104  traj.phases.coast.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        105  traj.phases.coast.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        106  traj.phases.coast.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        107  traj.phases.coast.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        108  traj.phases.coast.continuity_comp.defect_states:vt                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        109  traj.phases.coast.continuity_comp.defect_states:vt                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        110  traj.phases.coast.continuity_comp.defect_states:vt                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        111  traj.phases.coast.continuity_comp.defect_states:vt                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        112  traj.phases.coast.continuity_comp.defect_states:accel              e   0.000000E+00    7.298869E-35    0.000000E+00              9.00000E+100
        113  traj.phases.coast.continuity_comp.defect_states:accel              e   0.000000E+00   -2.959874E-34    0.000000E+00              9.00000E+100
        114  traj.phases.coast.continuity_comp.defect_states:accel              e   0.000000E+00   -2.549616E-34    0.000000E+00              9.00000E+100
        115  traj.phases.coast.continuity_comp.defect_states:accel              e   0.000000E+00   -2.069887E-34    0.000000E+00              9.00000E+100
        116  traj.phases.coast.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        117  traj.phases.coast.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        118  traj.phases.coast.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        119  traj.phases.coast.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        120  traj.phases.burn2.collocation_constraint.defects:r                 e   0.000000E+00    3.579330E-14    0.000000E+00              9.00000E+100
        121  traj.phases.burn2.collocation_constraint.defects:r                 e   0.000000E+00   -3.296169E-14    0.000000E+00              9.00000E+100
        122  traj.phases.burn2.collocation_constraint.defects:r                 e   0.000000E+00    7.486065E-14    0.000000E+00              9.00000E+100
        123  traj.phases.burn2.collocation_constraint.defects:r                 e   0.000000E+00   -4.851342E-14    0.000000E+00              9.00000E+100
        124  traj.phases.burn2.collocation_constraint.defects:r                 e   0.000000E+00    2.813634E-15    0.000000E+00              9.00000E+100
        125  traj.phases.burn2.collocation_constraint.defects:theta             e   0.000000E+00    4.459783E-14    0.000000E+00              9.00000E+100
        126  traj.phases.burn2.collocation_constraint.defects:theta             e   0.000000E+00    1.238829E-14    0.000000E+00              9.00000E+100
        127  traj.phases.burn2.collocation_constraint.defects:theta             e   0.000000E+00   -1.521990E-14    0.000000E+00              9.00000E+100
        128  traj.phases.burn2.collocation_constraint.defects:theta             e   0.000000E+00   -1.946731E-14    0.000000E+00              9.00000E+100
        129  traj.phases.burn2.collocation_constraint.defects:theta             e   0.000000E+00    3.291745E-14    0.000000E+00              9.00000E+100
        130  traj.phases.burn2.collocation_constraint.defects:vr                e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        131  traj.phases.burn2.collocation_constraint.defects:vr                e   0.000000E+00    7.079021E-15    0.000000E+00              9.00000E+100
        132  traj.phases.burn2.collocation_constraint.defects:vr                e   0.000000E+00    4.424388E-16    0.000000E+00              9.00000E+100
        133  traj.phases.burn2.collocation_constraint.defects:vr                e   0.000000E+00   -7.963899E-15    0.000000E+00              9.00000E+100
        134  traj.phases.burn2.collocation_constraint.defects:vr                e   0.000000E+00    3.760730E-15    0.000000E+00              9.00000E+100
        135  traj.phases.burn2.collocation_constraint.defects:vt                e   0.000000E+00   -2.831608E-14    0.000000E+00              9.00000E+100
        136  traj.phases.burn2.collocation_constraint.defects:vt                e   0.000000E+00    3.539511E-14    0.000000E+00              9.00000E+100
        137  traj.phases.burn2.collocation_constraint.defects:vt                e   0.000000E+00   -1.769755E-15    0.000000E+00              9.00000E+100
        138  traj.phases.burn2.collocation_constraint.defects:vt                e   0.000000E+00    1.061853E-14    0.000000E+00              9.00000E+100
        139  traj.phases.burn2.collocation_constraint.defects:vt                e   0.000000E+00   -1.061853E-14    0.000000E+00              9.00000E+100
        140  traj.phases.burn2.collocation_constraint.defects:accel             e   0.000000E+00   -7.079021E-18    0.000000E+00              9.00000E+100
        141  traj.phases.burn2.collocation_constraint.defects:accel             e   0.000000E+00   -1.106097E-18    0.000000E+00              9.00000E+100
        142  traj.phases.burn2.collocation_constraint.defects:accel             e   0.000000E+00    3.760730E-18    0.000000E+00              9.00000E+100
        143  traj.phases.burn2.collocation_constraint.defects:accel             e   0.000000E+00    1.194585E-17    0.000000E+00              9.00000E+100
        144  traj.phases.burn2.collocation_constraint.defects:accel             e   0.000000E+00   -1.570658E-17    0.000000E+00              9.00000E+100
        145  traj.phases.burn2.collocation_constraint.defects:deltav            e   0.000000E+00   -3.716486E-17    0.000000E+00              9.00000E+100
        146  traj.phases.burn2.collocation_constraint.defects:deltav            e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        147  traj.phases.burn2.collocation_constraint.defects:deltav            e   0.000000E+00    6.371119E-17    0.000000E+00              9.00000E+100
        148  traj.phases.burn2.collocation_constraint.defects:deltav            e   0.000000E+00    3.539511E-18    0.000000E+00              9.00000E+100
        149  traj.phases.burn2.collocation_constraint.defects:deltav            e   0.000000E+00   -1.769755E-17    0.000000E+00              9.00000E+100
        150  traj.phases.burn2.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        151  traj.phases.burn2.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        152  traj.phases.burn2.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        153  traj.phases.burn2.continuity_comp.defect_states:r                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        154  traj.phases.burn2.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        155  traj.phases.burn2.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        156  traj.phases.burn2.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        157  traj.phases.burn2.continuity_comp.defect_states:theta              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        158  traj.phases.burn2.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        159  traj.phases.burn2.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        160  traj.phases.burn2.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        161  traj.phases.burn2.continuity_comp.defect_states:vr                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        162  traj.phases.burn2.continuity_comp.defect_states:vt                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        163  traj.phases.burn2.continuity_comp.defect_states:vt                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        164  traj.phases.burn2.continuity_comp.defect_states:vt                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        165  traj.phases.burn2.continuity_comp.defect_states:vt                 e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        166  traj.phases.burn2.continuity_comp.defect_states:accel              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        167  traj.phases.burn2.continuity_comp.defect_states:accel              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        168  traj.phases.burn2.continuity_comp.defect_states:accel              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        169  traj.phases.burn2.continuity_comp.defect_states:accel              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        170  traj.phases.burn2.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        171  traj.phases.burn2.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        172  traj.phases.burn2.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        173  traj.phases.burn2.continuity_comp.defect_states:deltav             e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        174  traj.phases.burn2.continuity_comp.defect_controls:u1               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        175  traj.phases.burn2.continuity_comp.defect_controls:u1               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        176  traj.phases.burn2.continuity_comp.defect_controls:u1               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        177  traj.phases.burn2.continuity_comp.defect_controls:u1               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        178  traj.phases.burn2.continuity_comp.defect_control_rates:u1_rate     e   0.000000E+00   -1.132643E-15    0.000000E+00              9.00000E+100
        179  traj.phases.burn2.continuity_comp.defect_control_rates:u1_rate     e   0.000000E+00   -1.415804E-15    0.000000E+00              9.00000E+100
        180  traj.phases.burn2.continuity_comp.defect_control_rates:u1_rate     e   0.000000E+00    7.255997E-16    0.000000E+00              9.00000E+100
        181  traj.phases.burn2.continuity_comp.defect_control_rates:u1_rate     e   0.000000E+00   -2.229892E-15    0.000000E+00              9.00000E+100
        182  traj.phases.burn2.continuity_comp.defect_control_rates:u1_rate2    e   0.000000E+00   -8.305275E-15    0.000000E+00              9.00000E+100
        183  traj.phases.burn2.continuity_comp.defect_control_rates:u1_rate2    e   0.000000E+00   -9.027473E-16    0.000000E+00              9.00000E+100
        184  traj.phases.burn2.continuity_comp.defect_control_rates:u1_rate2    e   0.000000E+00    4.333187E-15    0.000000E+00              9.00000E+100
        185  traj.phases.burn2.continuity_comp.defect_control_rates:u1_rate2    e   0.000000E+00   -2.888791E-15    0.000000E+00              9.00000E+100
        186  traj.linkages.burn1:time_final|coast:time_initial                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        187  traj.linkages.burn1:r_final|coast:r_initial                        e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        188  traj.linkages.burn1:theta_final|coast:theta_initial                e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        189  traj.linkages.burn1:vr_final|coast:vr_initial                      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        190  traj.linkages.burn1:vt_final|coast:vt_initial                      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        191  traj.linkages.burn1:deltav_final|coast:deltav_initial              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        192  traj.linkages.coast:time_final|burn2:time_initial                  e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        193  traj.linkages.coast:r_final|burn2:r_initial                        e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        194  traj.linkages.coast:theta_final|burn2:theta_initial                e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        195  traj.linkages.coast:vr_final|burn2:vr_initial                      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        196  traj.linkages.coast:vt_final|burn2:vt_initial                      e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        197  traj.linkages.coast:deltav_final|burn2:deltav_initial              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        198  traj.linkages.burn1:accel_final|burn2:accel_initial                e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100

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


Simulating trajectory traj
Done simulating trajectory traj

References


  1. Paul J Enright and Brace A Conway. Optimal finite-thrust spacecraft trajectories using collocation and nonlinear programming. Journal of Guidance, Control, and Dynamics, 145:981–985, 1991.