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Single-Phase Space Shuttle Reentry

The problem of the space shuttle reentering Earth's atmosphere is an optimal control problem governed by six equations of motion and limited by the aerodynamic heating rate. For a detailed layout of this problem and other optimal control problems see Betts1. The governing equations of motion for this problem are:

\begin{align} \frac{dh}{dt} &= v \sin \gamma \\ \frac{d\phi}{dt} &= \frac{v}{r} \cos \gamma \frac{\sin \psi}{\cos \theta} \\ \frac{d\theta}{dt} &= \frac{v}{r} \cos \gamma \cos \psi \\ \frac{dv}{dt} &= - \frac{D}{m} - g \sin \gamma \\ \frac{d\gamma}{dt} &= \frac{L}{mv} \cos \beta + \cos \gamma (\frac{v}{r} - \frac{g}{v}) \\ \frac{d\psi}{dt} &= \frac{L \sin \beta}{mv \cos \gamma} + \frac{v}{r \cos \theta} \cos \gamma \sin \psi \sin \theta \end{align}

where v [ft/s] is airspeed, \gamma [rad] is flight path angle, r [ft] is distance from the center of the Earth, \psi [rad] is azimuth, \theta [rad] is latitude, D [lb] is drag, m [sl] is mass, g [\frac{ft}{s^2}] is the local gravitational acceleration, L [lb] is lift, \beta [rad] is bank angle, h [ft] is altitude, and \phi [rad] is longitude. Mass is considered to be a constant for this case, because the model spans the time from when the shuttle begins reentry to the time right before the shuttle starts its engines. The engines are not actually running at any time during the model, so there is no thrust and thus no mass lost. The goal is to maximize the crossrange (latitude) that the shuttle can cover before reaching the final altitude, without exceding a maximum heat rate at the leading edges. This heat rate is constrained by q \leq 70 where q [\frac{btu}{ft^2s}] is the heating rate.

The initial conditions are

\begin{align} h_0 &= 26000 \\ v_0 &= 25600 \\ \phi_0 &= 0 \\ \gamma_0 &= -0.01745 \\ \theta_0 &= 0 \\ \psi_0 &= \frac{\pi}{2} \end{align}

and the final conditions are

\begin{align} h_0 &= 80000 \\ v_0 &= 2500 \\ \gamma_0 &= -0.08727 \\ \theta &= \rm{free} \\ \psi &= \rm{free} \end{align}

Notice that no final condition appears for \phi. This is because none of the equations of motion actually depend on \phi, and as a result, while \phi exists in the dymos model (last code block below) as a state variable, it does not exist as either an input or output in the ode (ShuttleODE group, second to last code block below).

This model uses four explicit OpenMDAO components. The first component computes the local atmospheric condition at the shuttle's altitude. The second component computes the aerodynamic forces of lift and drag on the shuttle. The third component is where the heating rate on the leading edge of the shuttles wings is computed. The heating rate is given by q = q_a q_r where

\begin{align} q_a &= c_0 + c_1\alpha + c_2 \alpha^2 + c_3 \alpha^3 \end{align}

and

\begin{align} q_r &= 17700 \rho^.5 (.0001v)^{3.07} \end{align}

where c_0, c_1, c_2, and c_3 are constants, \alpha [deg] is the angle of attack, \rho [\frac{sl}{ft^3}] is local atmospheric density, and v [\frac{ft}{s}] is velocity. The final component is where the equations of motion are implemented. These four components are put together in the ShuttleODE group, which is the top level ode that the dymos model sees.

Component Models

Below is the code for the atmospheric component:

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import numpy as np
import openmdao.api as om


class Atmosphere(om.ExplicitComponent):
    """
    Defines the logarithmic atmosphere model for the shuttle reentry problem.

    References
    ----------
    .. [1] Betts, John T., Practical Methods for Optimal Control and Estimation Using Nonlinear
           Programming, p. 248, 2010.
    """

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

    def setup(self):
        nn = self.options['num_nodes']
        self.add_input('h', val=np.ones(nn), desc='altitude', units='ft')
        self.add_output('rho', val=np.ones(nn), desc='local density', units='slug/ft**3')
        partial_range = np.arange(nn, dtype=int)
        self.declare_partials('rho', 'h', rows=partial_range, cols=partial_range)

    def compute(self, inputs, outputs):
        h = inputs['h']
        h_r = 23800
        rho_0 = .002378
        outputs['rho'] = rho_0 * np.exp(-h / h_r)

    def compute_partials(self, inputs, partials):
        h = inputs['h']
        h_r = 23800
        rho_0 = .002378
        partials['rho', 'h'] = -1 / h_r * rho_0 * np.exp(-h / h_r)

Below is the code for the aerodynamic component:

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import numpy as np
import openmdao.api as om


class Aerodynamics(om.ExplicitComponent):
    """
    Defines the aerodynamics for the shuttle reentry problem.

    References
    ----------
    .. [1] Betts, John T., Practical Methods for Optimal Control and Estimation Using Nonlinear
           Programming, p. 248, 2010.
    """

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

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

        self.add_input('alpha', val=np.ones(nn), desc='angle of attack', units='deg')
        self.add_input('v', val=np.ones(nn), desc='velocity of shuttle', units='ft/s')
        self.add_input('rho', val=np.ones(nn), desc='local atmospheric density',
                       units='slug/ft**3')

        self.add_output('drag', val=np.ones(nn), desc='drag on shuttle', units='lb')
        self.add_output('lift', val=np.ones(nn), desc='lift on shuttle', units='lb')

        partial_range = np.arange(nn, dtype=int)

        self.declare_partials('drag', 'alpha', rows=partial_range, cols=partial_range)
        self.declare_partials('drag', 'v', rows=partial_range, cols=partial_range)
        self.declare_partials('drag', 'rho', rows=partial_range, cols=partial_range)
        self.declare_partials('lift', 'alpha', rows=partial_range, cols=partial_range)
        self.declare_partials('lift', 'v', rows=partial_range, cols=partial_range)
        self.declare_partials('lift', 'rho', rows=partial_range, cols=partial_range)

    def compute(self, inputs, outputs):
        a_0 = -.20704
        a_1 = .029244
        b_0 = .07854
        b_1 = -.61592e-2
        b_2 = .621408e-3
        S = 2690
        alpha = inputs['alpha']
        v = inputs['v']
        rho = inputs['rho']
        c_L = a_0 + a_1 * alpha
        c_D = b_0 + b_1 * alpha + b_2 * alpha ** 2

        outputs['drag'] = .5 * c_D * S * rho * v ** 2
        outputs['lift'] = .5 * c_L * S * rho * v ** 2

    def compute_partials(self, inputs, J):
        alpha = inputs['alpha']
        v = inputs['v']
        rho = inputs['rho']
        a_0 = -.20704
        a_1 = .029244
        b_0 = .07854
        b_1 = -.61592e-2
        b_2 = .621408e-3
        S = 2690
        c_L = a_0 + a_1 * alpha
        c_D = b_0 + b_1 * alpha + b_2 * alpha ** 2

        dD_dCD = .5 * S * rho * v ** 2
        dCD_dalpha = b_1 + 2 * alpha * b_2
        dL_dCL = dD_dCD
        dCL_dalpha = a_1

        J['drag', 'alpha'] = dD_dCD * dCD_dalpha
        J['drag', 'v'] = c_D * S * rho * v
        J['drag', 'rho'] = .5 * c_D * S * v ** 2
        J['lift', 'alpha'] = dL_dCL * dCL_dalpha
        J['lift', 'v'] = c_L * S * rho * v
        J['lift', 'rho'] = .5 * c_L * S * v ** 2

Below is the code for the heating component:

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import numpy as np
import openmdao.api as om


class AerodynamicHeating(om.ExplicitComponent):
    """
    Defines the Aerodynamic heating equations for the shuttle reentry problem.

    References
    ----------
    .. [1] Betts, John T., Practical Methods for Optimal Control and Estimation Using Nonlinear
           Programming, p. 248, 2010.
    """

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

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

        self.add_input('rho', val=np.ones(nn), desc='local density', units='slug/ft**3')
        self.add_input('v', val=np.ones(nn), desc='velocity of shuttle', units='ft/s')
        self.add_input('alpha', val=np.ones(nn), desc='angle of attack of shuttle',
                       units='deg')

        self.add_output('q', val=np.ones(nn),
                        desc='aerodynamic heating on leading edge of shuttle',
                        units='Btu/ft**2/s')

        partial_range = np.arange(nn)

        self.declare_partials('q', 'rho', rows=partial_range, cols=partial_range)
        self.declare_partials('q', 'v', rows=partial_range, cols=partial_range)
        self.declare_partials('q', 'alpha', rows=partial_range, cols=partial_range)

    def compute(self, inputs, outputs):
        rho = inputs['rho']
        v = inputs['v']
        alpha = inputs['alpha']
        c_0 = 1.0672181
        c_1 = -0.19213774e-1
        c_2 = 0.21286289e-3
        c_3 = -0.10117249e-5

        if np.any(v < 0):
            raise om.AnalysisError('Negative velocity magnitude encountered')

        q_r = 17700.0 * np.sqrt(rho) * (0.0001 * v) ** 3.07
        q_a = c_0 + c_1 * alpha + c_2 * alpha ** 2 + c_3 * alpha ** 3

        outputs['q'] = q_r * q_a

    def compute_partials(self, inputs, partials):
        rho = inputs['rho']
        v = inputs['v']
        alpha = inputs['alpha']
        c_0 = 1.0672181
        c_1 = -.19213774e-1
        c_2 = .21286289e-3
        c_3 = -.10117249e-5

        if np.any(v < 0):
            raise om.AnalysisError('Negative velocity magnitude encountered')

        sqrt_rho = np.sqrt(rho)

        q_r = 17700 * sqrt_rho * (.0001 * v) ** 3.07
        q_a = c_0 + c_1 * alpha + c_2 * alpha ** 2 + c_3 * alpha ** 3

        dqr_drho = 0.5 * q_r / rho
        dqr_dv = 17700 * sqrt_rho * 0.0001 * 3.07 * (0.0001 * v) ** 2.07

        dqa_dalpha = c_1 + 2 * c_2 * alpha + 3 * c_3 * alpha ** 2

        partials['q', 'rho'] = dqr_drho * q_a
        partials['q', 'v'] = dqr_dv * q_a
        partials['q', 'alpha'] = dqa_dalpha * q_r

Below is the code for the component containing the equations of motion:

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import numpy as np
from openmdao.api import ExplicitComponent, Problem


class FlightDynamics(ExplicitComponent):
    """
    Defines the flight dynamics for the shuttle reentry problem.

    References
    ----------
    .. [1] Betts, John T., Practical Methods for Optimal Control and Estimation Using Nonlinear
           Programming, p. 247, 2010.
    """

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

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

        self.add_input('beta', val=np.ones(nn), desc='bank angle', units='rad')
        self.add_input('gamma', val=np.ones(nn), desc='flight path angle', units='rad')
        self.add_input('h', val=np.ones(nn), desc='altitude of shuttle', units='ft')
        self.add_input('psi', val=np.ones(nn), desc='azimuthal angle', units='rad')
        self.add_input('theta', val=np.ones(nn), desc='latitude', units='rad')
        self.add_input('v', val=np.ones(nn), desc='velocity of shuttle', units='ft/s')
        self.add_input('lift', val=np.ones(nn), desc='lift on shuttle', units='lb')
        self.add_input('drag', val=np.ones(nn), desc='drag on shuttle', units='lb')

        self.add_output('hdot', val=np.ones(nn), desc='rate of change of altitude',
                        units='ft/s')
        self.add_output('gammadot', val=np.ones(nn),
                        desc='rate of change of flight path angle', units='rad/s')
        self.add_output('phidot', val=np.ones(nn), desc='rate of change of longitude',
                        units='rad/s')
        self.add_output('psidot', val=np.ones(nn), desc='rate of change of azimuthal angle',
                        units='rad/s')
        self.add_output('thetadot', val=np.ones(nn), desc='rate of change of latitude',
                        units='rad/s')
        self.add_output('vdot', val=np.ones(nn), desc='rate of change of velocity',
                        units='ft/s**2')

        partial_range = np.arange(nn, dtype=int)

        self.declare_partials('hdot', 'v', rows=partial_range, cols=partial_range)
        self.declare_partials('hdot', 'gamma', rows=partial_range, cols=partial_range)

        self.declare_partials('gammadot', 'lift', rows=partial_range, cols=partial_range)
        self.declare_partials('gammadot', 'h', rows=partial_range, cols=partial_range)
        self.declare_partials('gammadot', 'beta', rows=partial_range, cols=partial_range)
        self.declare_partials('gammadot', 'gamma', rows=partial_range, cols=partial_range)
        self.declare_partials('gammadot', 'v', rows=partial_range, cols=partial_range)

        self.declare_partials('phidot', 'v', rows=partial_range, cols=partial_range)
        self.declare_partials('phidot', 'h', rows=partial_range, cols=partial_range)
        self.declare_partials('phidot', 'gamma', rows=partial_range, cols=partial_range)
        self.declare_partials('phidot', 'psi', rows=partial_range, cols=partial_range)
        self.declare_partials('phidot', 'theta', rows=partial_range, cols=partial_range)

        self.declare_partials('psidot', 'v', rows=partial_range, cols=partial_range)
        self.declare_partials('psidot', 'gamma', rows=partial_range, cols=partial_range)
        self.declare_partials('psidot', 'h', rows=partial_range, cols=partial_range)
        self.declare_partials('psidot', 'beta', rows=partial_range, cols=partial_range)
        self.declare_partials('psidot', 'theta', rows=partial_range, cols=partial_range)
        self.declare_partials('psidot', 'psi', rows=partial_range, cols=partial_range)
        self.declare_partials('psidot', 'lift', rows=partial_range, cols=partial_range)

        self.declare_partials('thetadot', 'v', rows=partial_range, cols=partial_range)
        self.declare_partials('thetadot', 'h', rows=partial_range, cols=partial_range)
        self.declare_partials('thetadot', 'gamma', rows=partial_range, cols=partial_range)
        self.declare_partials('thetadot', 'psi', rows=partial_range, cols=partial_range)

        self.declare_partials('vdot', 'drag', rows=partial_range, cols=partial_range)
        self.declare_partials('vdot', 'gamma', rows=partial_range, cols=partial_range)
        self.declare_partials('vdot', 'h', rows=partial_range, cols=partial_range)

    def compute(self, inputs, outputs):
        v = inputs['v']
        gamma = inputs['gamma']
        theta = inputs['theta']
        lift = inputs['lift']
        drag = inputs['drag']
        h = inputs['h']
        beta = inputs['beta']
        psi = inputs['psi']
        g_0 = 32.174
        w = 203000
        R_e = 20902900
        mu = .14076539e17
        s_beta = np.sin(beta)
        c_beta = np.cos(beta)
        s_gamma = np.sin(gamma)
        c_gamma = np.cos(gamma)
        s_psi = np.sin(psi)
        c_psi = np.cos(psi)
        c_theta = np.cos(theta)
        s_theta = np.sin(theta)
        r = R_e + h
        m = w / g_0
        g = mu / r ** 2

        outputs['hdot'] = v * s_gamma
        outputs['gammadot'] = lift / (m * v) * c_beta + c_gamma * (v / r - g / v)
        outputs['phidot'] = v / r * c_gamma * s_psi / c_theta
        outputs['psidot'] = lift * s_beta / (m * v * c_gamma) + \
            v * c_gamma * s_psi * s_theta / (r * c_theta)
        outputs['thetadot'] = c_gamma * c_psi * v / r
        outputs['vdot'] = -drag / m - g * s_gamma

    def compute_partials(self, inputs, J):
        v = inputs['v']
        gamma = inputs['gamma']
        theta = inputs['theta']
        lift = inputs['lift']
        h = inputs['h']
        beta = inputs['beta']
        psi = inputs['psi']
        g_0 = 32.174
        w = 203000
        R_e = 20902900
        mu = .14076539e17
        s_beta = np.sin(beta)
        c_beta = np.cos(beta)
        s_gamma = np.sin(gamma)
        c_gamma = np.cos(gamma)
        s_psi = np.sin(psi)
        c_psi = np.cos(psi)
        c_theta = np.cos(theta)
        s_theta = np.sin(theta)
        r = R_e + h
        m = w / g_0
        g = mu / r ** 2

        J['hdot', 'v'] = s_gamma
        J['hdot', 'gamma'] = v * c_gamma

        J['gammadot', 'lift'] = c_beta / (m * v)
        J['gammadot', 'h'] = c_gamma * (-v / r ** 2 + 2 * mu / (r ** 3 * v))
        J['gammadot', 'beta'] = -lift / (m * v) * s_beta
        J['gammadot', 'gamma'] = -s_gamma * (v / r - g / v)
        J['gammadot', 'v'] = -lift / (m * v ** 2) * c_beta + c_gamma * (1 / r + g / v ** 2)

        J['phidot', 'v'] = c_gamma * s_psi / (c_theta * r)
        J['phidot', 'h'] = -v / r ** 2 * c_gamma * s_psi / c_theta
        J['phidot', 'gamma'] = -v / r * s_gamma * s_psi / c_theta
        J['phidot', 'psi'] = v / r * c_gamma * c_psi / c_theta
        J['phidot', 'theta'] = v / r * c_gamma * s_psi / (c_theta ** 2) * s_theta

        J['psidot', 'v'] = -lift * s_beta / (m * c_gamma * v ** 2) + \
            c_gamma * s_psi * s_theta / (r * c_theta)
        J['psidot', 'gamma'] = lift * s_beta / (m * v * c_gamma ** 2) * s_gamma - \
            v * s_gamma * s_psi * s_theta / (r * c_theta)
        J['psidot', 'h'] = -v * c_gamma * s_psi * s_theta / (c_theta * r ** 2)
        J['psidot', 'beta'] = lift * c_beta / (m * v * c_gamma)
        J['psidot', 'theta'] = v * c_gamma * s_psi / (r * c_theta ** 2)
        J['psidot', 'psi'] = v * c_gamma * c_psi * s_theta / (r * c_theta)
        J['psidot', 'lift'] = s_beta / (m * v * c_gamma)

        J['thetadot', 'v'] = c_gamma * c_psi / r
        J['thetadot', 'h'] = -v / r ** 2 * c_gamma * c_psi
        J['thetadot', 'gamma'] = -v / r * s_gamma * c_psi
        J['thetadot', 'psi'] = -v / r * c_gamma * s_psi

        J['vdot', 'h'] = 2 * s_gamma * mu / r ** 3
        J['vdot', 'drag'] = -1 / m
        J['vdot', 'gamma'] = -g * c_gamma

Defining the ODE

Below is the code for the top level ode group that will be fed to dymos:

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from openmdao.api import Problem, Group
from dymos.examples.shuttle_reentry.heating_comp import AerodynamicHeating
from dymos.examples.shuttle_reentry.flight_dynamics_comp import FlightDynamics
from dymos.examples.shuttle_reentry.aerodynamics_comp import Aerodynamics
from dymos.examples.shuttle_reentry.atmosphere_comp import Atmosphere


class ShuttleODE(Group):
    """
    The ODE for the Shuttle reentry problem.

    References
    ----------
    .. [1] Betts, John T., Practical Methods for Optimal Control and Estimation Using Nonlinear
           Programming, p. 248, 2010.
    """

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

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

        self.add_subsystem('atmosphere', subsys=Atmosphere(num_nodes=nn),
                           promotes_inputs=['h'], promotes_outputs=['rho'])
        self.add_subsystem('aerodynamics', subsys=Aerodynamics(num_nodes=nn),
                           promotes_inputs=['alpha', 'v', 'rho'],
                           promotes_outputs=['lift', 'drag'])
        self.add_subsystem('heating', subsys=AerodynamicHeating(num_nodes=nn),
                           promotes_inputs=['rho', 'v', 'alpha'], promotes_outputs=['q'])
        self.add_subsystem('eom', subsys=FlightDynamics(num_nodes=nn),
                           promotes_inputs=['beta', 'gamma', 'h', 'psi', 'theta', 'v', 'lift',
                                            'drag'],
                           promotes_outputs=['hdot', 'gammadot', 'phidot', 'psidot', 'thetadot',
                                             'vdot'])

Building and running the problem

The following code is the dymos implementation of the model. As the code shows, there are six states, two controls, and one constraint in the model. The states are h, v, \phi, \gamma, \theta, and \psi. The two controls are \alpha and \beta, and the constraint is q.

import openmdao.api as om
from openmdao.utils.assert_utils import assert_near_equal
import dymos as dm
from dymos.examples.shuttle_reentry.shuttle_ode import ShuttleODE
from dymos.examples.plotting import plot_results

# Instantiate the problem, add the driver, and allow it to use coloring
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.declare_coloring()
p.driver.options['optimizer'] = 'SLSQP'

# Instantiate the trajectory and add a phase to it
traj = p.model.add_subsystem('traj', dm.Trajectory())
phase0 = traj.add_phase('phase0',
                        dm.Phase(ode_class=ShuttleODE,
                                 transcription=dm.Radau(num_segments=15, order=3)))

phase0.set_time_options(fix_initial=True, units='s', duration_ref=200)
phase0.add_state('h', fix_initial=True, fix_final=True, units='ft', rate_source='hdot',
                 lower=0, ref0=75000, ref=300000, defect_ref=1000)
phase0.add_state('gamma', fix_initial=True, fix_final=True, units='rad',
                 rate_source='gammadot',
                 lower=-89. * np.pi / 180, upper=89. * np.pi / 180)
phase0.add_state('phi', fix_initial=True, fix_final=False, units='rad',
                 rate_source='phidot', lower=0, upper=89. * np.pi / 180)
phase0.add_state('psi', fix_initial=True, fix_final=False, units='rad',
                 rate_source='psidot', lower=0, upper=90. * np.pi / 180)
phase0.add_state('theta', fix_initial=True, fix_final=False, units='rad',
                 rate_source='thetadot',
                 lower=-89. * np.pi / 180, upper=89. * np.pi / 180)
phase0.add_state('v', fix_initial=True, fix_final=True, units='ft/s',
                 rate_source='vdot', lower=0, ref0=2500, ref=25000)
phase0.add_control('alpha', units='rad', opt=True, lower=-np.pi / 2, upper=np.pi / 2, )
phase0.add_control('beta', units='rad', opt=True, lower=-89 * np.pi / 180, upper=1 * np.pi / 180, )

# The original implementation by Betts includes a heating rate path constraint.
# This will work with the SNOPT optimizer but SLSQP has difficulty converging the solution.
# phase0.add_path_constraint('q', lower=0, upper=70, ref=70)
phase0.add_timeseries_output('q', shape=(1,))

phase0.add_objective('theta', loc='final', ref=-0.01)

p.setup(check=True)

p.set_val('traj.phase0.states:h',
          phase0.interpolate(ys=[260000, 80000], nodes='state_input'), units='ft')
p.set_val('traj.phase0.states:gamma',
          phase0.interpolate(ys=[-1, -5], nodes='state_input'), units='deg')
p.set_val('traj.phase0.states:phi',
          phase0.interpolate(ys=[0, 75], nodes='state_input'), units='deg')
p.set_val('traj.phase0.states:psi',
          phase0.interpolate(ys=[90, 10], nodes='state_input'), units='deg')
p.set_val('traj.phase0.states:theta',
          phase0.interpolate(ys=[0, 25], nodes='state_input'), units='deg')
p.set_val('traj.phase0.states:v',
          phase0.interpolate(ys=[25600, 2500], nodes='state_input'), units='ft/s')
p.set_val('traj.phase0.t_initial', 0, units='s')
p.set_val('traj.phase0.t_duration', 2000, units='s')
p.set_val('traj.phase0.controls:alpha',
          phase0.interpolate(ys=[17.4, 17.4], nodes='control_input'), units='deg')
p.set_val('traj.phase0.controls:beta',
          phase0.interpolate(ys=[-75, 0], nodes='control_input'), units='deg')

# Run the driver
dm.run_problem(p)

# Check the validity of the solution


# assert_near_equal(p.get_val('traj.phase0.timeseries.time')[-1], 2181.90371131, tolerance=1e-3)
# assert_near_equal(p.get_val('traj.phase0.timeseries.states:theta')[-1], .53440626, tolerance=1e-3)

# Run the simulation to check if the model is physically valid
sim_out = traj.simulate()

# Plot the results

plot_results([('traj.phase0.timeseries.time', 'traj.phase0.timeseries.controls:alpha',
               'time (s)', 'alpha (rad)'),
              ('traj.phase0.timeseries.time', 'traj.phase0.timeseries.controls:beta',
               'time (s)', 'beta (rad)'),
              ('traj.phase0.timeseries.time', 'traj.phase0.timeseries.states:theta',
               'time (s)', 'theta (rad)'),
              ('traj.phase0.timeseries.time', 'traj.phase0.timeseries.q',
               'time (s)', 'q (btu/ft/ft/s')], title='Reentry Solution', p_sol=p,
             p_sim=sim_out)

plt.show()
INFO: checking out_of_order
INFO: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
INFO: checking out_of_order
INFO: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
INFO: checking out_of_order
INFO: checking system
INFO: checking solvers
INFO: checking dup_inputs
INFO: checking missing_recorders
WARNING: The Problem has no recorder of any kind attached
INFO: checking comp_has_no_outputs
INFO: checking auto_ivc_warnings
Full total jacobian was computed 3 times, taking 0.730299 seconds.
Total jacobian shape: (327, 358) 


Jacobian shape: (327, 358)  ( 2.83% nonzero)
FWD solves: 1   REV solves: 24
Total colors vs. total size: 25 vs 327  (92.4% improvement)

Sparsity computed using tolerance: 1e-25
Time to compute sparsity: 0.730299 sec.
Time to compute coloring: 0.054621 sec.


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

    Solution: 
--------------------------------------------------------------------------------
    Total Time:                   61.1769
       User Objective Time :       2.5447
       User Sensitivity Time :     8.1278
       Interface Time :            4.5400
       Opt Solver Time:           45.9644
    Calls to Objective Function :     750
    Calls to Sens Function :          316


   Objectives
      Index  Name                                                    Value          Optimum
          0  traj.phases.phase0.indep_states.states:theta    -5.957515E+01     0.000000E+00

   Variables (c - continuous, i - integer, d - discrete)
      Index  Name                                                                Type      Lower Bound            Value      Upper Bound     Status
          0  traj.phases.phase0.time_extents.t_duration_0                           c    -5.000000E+18     1.004110E+01     5.000000E+18           
          1  traj.phases.phase0.indep_states.states:h_0                             c    -3.333333E-01     7.284191E-01     4.444444E+15           
          2  traj.phases.phase0.indep_states.states:h_1                             c    -3.333333E-01     6.156008E-01     4.444444E+15           
          3  traj.phases.phase0.indep_states.states:h_2                             c    -3.333333E-01     5.881059E-01     4.444444E+15           
          4  traj.phases.phase0.indep_states.states:h_3                             c    -3.333333E-01     5.548430E-01     4.444444E+15           
          5  traj.phases.phase0.indep_states.states:h_4                             c    -3.333333E-01     5.678672E-01     4.444444E+15           
          6  traj.phases.phase0.indep_states.states:h_5                             c    -3.333333E-01     5.831732E-01     4.444444E+15           
          7  traj.phases.phase0.indep_states.states:h_6                             c    -3.333333E-01     6.122391E-01     4.444444E+15           
          8  traj.phases.phase0.indep_states.states:h_7                             c    -3.333333E-01     6.266081E-01     4.444444E+15           
          9  traj.phases.phase0.indep_states.states:h_8                             c    -3.333333E-01     6.207006E-01     4.444444E+15           
         10  traj.phases.phase0.indep_states.states:h_9                             c    -3.333333E-01     5.951172E-01     4.444444E+15           
         11  traj.phases.phase0.indep_states.states:h_10                            c    -3.333333E-01     5.501215E-01     4.444444E+15           
         12  traj.phases.phase0.indep_states.states:h_11                            c    -3.333333E-01     5.391189E-01     4.444444E+15           
         13  traj.phases.phase0.indep_states.states:h_12                            c    -3.333333E-01     5.282502E-01     4.444444E+15           
         14  traj.phases.phase0.indep_states.states:h_13                            c    -3.333333E-01     5.314316E-01     4.444444E+15           
         15  traj.phases.phase0.indep_states.states:h_14                            c    -3.333333E-01     5.334010E-01     4.444444E+15           
         16  traj.phases.phase0.indep_states.states:h_15                            c    -3.333333E-01     5.294726E-01     4.444444E+15           
         17  traj.phases.phase0.indep_states.states:h_16                            c    -3.333333E-01     5.100351E-01     4.444444E+15           
         18  traj.phases.phase0.indep_states.states:h_17                            c    -3.333333E-01     5.014708E-01     4.444444E+15           
         19  traj.phases.phase0.indep_states.states:h_18                            c    -3.333333E-01     4.869362E-01     4.444444E+15           
         20  traj.phases.phase0.indep_states.states:h_19                            c    -3.333333E-01     4.779910E-01     4.444444E+15           
         21  traj.phases.phase0.indep_states.states:h_20                            c    -3.333333E-01     4.777623E-01     4.444444E+15           
         22  traj.phases.phase0.indep_states.states:h_21                            c    -3.333333E-01     4.726679E-01     4.444444E+15           
         23  traj.phases.phase0.indep_states.states:h_22                            c    -3.333333E-01     4.551023E-01     4.444444E+15           
         24  traj.phases.phase0.indep_states.states:h_23                            c    -3.333333E-01     4.468736E-01     4.444444E+15           
         25  traj.phases.phase0.indep_states.states:h_24                            c    -3.333333E-01     4.317122E-01     4.444444E+15           
         26  traj.phases.phase0.indep_states.states:h_25                            c    -3.333333E-01     4.192299E-01     4.444444E+15           
         27  traj.phases.phase0.indep_states.states:h_26                            c    -3.333333E-01     4.173276E-01     4.444444E+15           
         28  traj.phases.phase0.indep_states.states:h_27                            c    -3.333333E-01     4.089229E-01     4.444444E+15           
         29  traj.phases.phase0.indep_states.states:h_28                            c    -3.333333E-01     3.894594E-01     4.444444E+15           
         30  traj.phases.phase0.indep_states.states:h_29                            c    -3.333333E-01     3.816296E-01     4.444444E+15           
         31  traj.phases.phase0.indep_states.states:h_30                            c    -3.333333E-01     3.661359E-01     4.444444E+15           
         32  traj.phases.phase0.indep_states.states:h_31                            c    -3.333333E-01     3.470245E-01     4.444444E+15           
         33  traj.phases.phase0.indep_states.states:h_32                            c    -3.333333E-01     3.409032E-01     4.444444E+15           
         34  traj.phases.phase0.indep_states.states:h_33                            c    -3.333333E-01     3.245237E-01     4.444444E+15           
         35  traj.phases.phase0.indep_states.states:h_34                            c    -3.333333E-01     2.998869E-01     4.444444E+15           
         36  traj.phases.phase0.indep_states.states:h_35                            c    -3.333333E-01     2.920840E-01     4.444444E+15           
         37  traj.phases.phase0.indep_states.states:h_36                            c    -3.333333E-01     2.727918E-01     4.444444E+15           
         38  traj.phases.phase0.indep_states.states:h_37                            c    -3.333333E-01     2.423669E-01     4.444444E+15           
         39  traj.phases.phase0.indep_states.states:h_38                            c    -3.333333E-01     2.319461E-01     4.444444E+15           
         40  traj.phases.phase0.indep_states.states:h_39                            c    -3.333333E-01     2.076305E-01     4.444444E+15           
         41  traj.phases.phase0.indep_states.states:h_40                            c    -3.333333E-01     1.650869E-01     4.444444E+15           
         42  traj.phases.phase0.indep_states.states:h_41                            c    -3.333333E-01     1.477299E-01     4.444444E+15           
         43  traj.phases.phase0.indep_states.states:h_42                            c    -3.333333E-01     1.041475E-01     4.444444E+15           
         44  traj.phases.phase0.indep_states.states:h_43                            c    -3.333333E-01     4.170888E-02     4.444444E+15           
         45  traj.phases.phase0.indep_states.states:gamma_0                         c    -1.553343E+00    -1.691945E-02     1.553343E+00           
         46  traj.phases.phase0.indep_states.states:gamma_1                         c    -1.553343E+00    -1.283402E-02     1.553343E+00           
         47  traj.phases.phase0.indep_states.states:gamma_2                         c    -1.553343E+00    -1.024640E-02     1.553343E+00           
         48  traj.phases.phase0.indep_states.states:gamma_3                         c    -1.553343E+00    -2.576351E-03     1.553343E+00           
         49  traj.phases.phase0.indep_states.states:gamma_4                         c    -1.553343E+00     5.866321E-03     1.553343E+00           
         50  traj.phases.phase0.indep_states.states:gamma_5                         c    -1.553343E+00     6.441738E-03     1.553343E+00           
         51  traj.phases.phase0.indep_states.states:gamma_6                         c    -1.553343E+00     4.808110E-03     1.553343E+00           
         52  traj.phases.phase0.indep_states.states:gamma_7                         c    -1.553343E+00    -1.356289E-03     1.553343E+00           
         53  traj.phases.phase0.indep_states.states:gamma_8                         c    -1.553343E+00    -3.429261E-03     1.553343E+00           
         54  traj.phases.phase0.indep_states.states:gamma_9                         c    -1.553343E+00    -6.650896E-03     1.553343E+00           
         55  traj.phases.phase0.indep_states.states:gamma_10                        c    -1.553343E+00    -6.058937E-03     1.553343E+00           
         56  traj.phases.phase0.indep_states.states:gamma_11                        c    -1.553343E+00    -4.306942E-03     1.553343E+00           
         57  traj.phases.phase0.indep_states.states:gamma_12                        c    -1.553343E+00    -7.065520E-04     1.553343E+00           
         58  traj.phases.phase0.indep_states.states:gamma_13                        c    -1.553343E+00     1.113422E-03     1.553343E+00           
         59  traj.phases.phase0.indep_states.states:gamma_14                        c    -1.553343E+00     3.157743E-04     1.553343E+00           
         60  traj.phases.phase0.indep_states.states:gamma_15                        c    -1.553343E+00    -2.061391E-03     1.553343E+00           
         61  traj.phases.phase0.indep_states.states:gamma_16                        c    -1.553343E+00    -4.489667E-03     1.553343E+00           
         62  traj.phases.phase0.indep_states.states:gamma_17                        c    -1.553343E+00    -4.409625E-03     1.553343E+00           
         63  traj.phases.phase0.indep_states.states:gamma_18                        c    -1.553343E+00    -2.799340E-03     1.553343E+00           
         64  traj.phases.phase0.indep_states.states:gamma_19                        c    -1.553343E+00    -5.095840E-04     1.553343E+00           
         65  traj.phases.phase0.indep_states.states:gamma_20                        c    -1.553343E+00    -5.390644E-04     1.553343E+00           
         66  traj.phases.phase0.indep_states.states:gamma_21                        c    -1.553343E+00    -2.269778E-03     1.553343E+00           
         67  traj.phases.phase0.indep_states.states:gamma_22                        c    -1.553343E+00    -5.014902E-03     1.553343E+00           
         68  traj.phases.phase0.indep_states.states:gamma_23                        c    -1.553343E+00    -5.208651E-03     1.553343E+00           
         69  traj.phases.phase0.indep_states.states:gamma_24                        c    -1.553343E+00    -3.855303E-03     1.553343E+00           
         70  traj.phases.phase0.indep_states.states:gamma_25                        c    -1.553343E+00    -1.783680E-03     1.553343E+00           
         71  traj.phases.phase0.indep_states.states:gamma_26                        c    -1.553343E+00    -1.910993E-03     1.553343E+00           
         72  traj.phases.phase0.indep_states.states:gamma_27                        c    -1.553343E+00    -3.800152E-03     1.553343E+00           
         73  traj.phases.phase0.indep_states.states:gamma_28                        c    -1.553343E+00    -6.349520E-03     1.553343E+00           
         74  traj.phases.phase0.indep_states.states:gamma_29                        c    -1.553343E+00    -6.414062E-03     1.553343E+00           
         75  traj.phases.phase0.indep_states.states:gamma_30                        c    -1.553343E+00    -5.815659E-03     1.553343E+00           
         76  traj.phases.phase0.indep_states.states:gamma_31                        c    -1.553343E+00    -6.071819E-03     1.553343E+00           
         77  traj.phases.phase0.indep_states.states:gamma_32                        c    -1.553343E+00    -6.897368E-03     1.553343E+00           
         78  traj.phases.phase0.indep_states.states:gamma_33                        c    -1.553343E+00    -8.398221E-03     1.553343E+00           
         79  traj.phases.phase0.indep_states.states:gamma_34                        c    -1.553343E+00    -9.727920E-03     1.553343E+00           
         80  traj.phases.phase0.indep_states.states:gamma_35                        c    -1.553343E+00    -1.009477E-02     1.553343E+00           
         81  traj.phases.phase0.indep_states.states:gamma_36                        c    -1.553343E+00    -1.259784E-02     1.553343E+00           
         82  traj.phases.phase0.indep_states.states:gamma_37                        c    -1.553343E+00    -1.655361E-02     1.553343E+00           
         83  traj.phases.phase0.indep_states.states:gamma_38                        c    -1.553343E+00    -1.734759E-02     1.553343E+00           
         84  traj.phases.phase0.indep_states.states:gamma_39                        c    -1.553343E+00    -2.174943E-02     1.553343E+00           
         85  traj.phases.phase0.indep_states.states:gamma_40                        c    -1.553343E+00    -3.753810E-02     1.553343E+00           
         86  traj.phases.phase0.indep_states.states:gamma_41                        c    -1.553343E+00    -4.531682E-02     1.553343E+00           
         87  traj.phases.phase0.indep_states.states:gamma_42                        c    -1.553343E+00    -5.728466E-02     1.553343E+00           
         88  traj.phases.phase0.indep_states.states:gamma_43                        c    -1.553343E+00    -7.670882E-02     1.553343E+00           
         89  traj.phases.phase0.indep_states.states:phi_0                           c     0.000000E+00     5.749110E-02     1.553343E+00           
         90  traj.phases.phase0.indep_states.states:phi_1                           c     0.000000E+00     1.364668E-01     1.553343E+00           
         91  traj.phases.phase0.indep_states.states:phi_2                           c     0.000000E+00     1.612787E-01     1.553343E+00           
         92  traj.phases.phase0.indep_states.states:phi_3                           c     0.000000E+00     2.173287E-01     1.553343E+00           
         93  traj.phases.phase0.indep_states.states:phi_4                           c     0.000000E+00     2.926138E-01     1.553343E+00           
         94  traj.phases.phase0.indep_states.states:phi_5                           c     0.000000E+00     3.158808E-01     1.553343E+00           
         95  traj.phases.phase0.indep_states.states:phi_6                           c     0.000000E+00     3.685302E-01     1.553343E+00           
         96  traj.phases.phase0.indep_states.states:phi_7                           c     0.000000E+00     4.398748E-01     1.553343E+00           
         97  traj.phases.phase0.indep_states.states:phi_8                           c     0.000000E+00     4.622100E-01     1.553343E+00           
         98  traj.phases.phase0.indep_states.states:phi_9                           c     0.000000E+00     5.128394E-01     1.553343E+00           
         99  traj.phases.phase0.indep_states.states:phi_10                          c     0.000000E+00     5.812205E-01     1.553343E+00           
        100  traj.phases.phase0.indep_states.states:phi_11                          c     0.000000E+00     6.024128E-01     1.553343E+00           
        101  traj.phases.phase0.indep_states.states:phi_12                          c     0.000000E+00     6.498681E-01     1.553343E+00           
        102  traj.phases.phase0.indep_states.states:phi_13                          c     0.000000E+00     7.128992E-01     1.553343E+00           
        103  traj.phases.phase0.indep_states.states:phi_14                          c     0.000000E+00     7.322549E-01     1.553343E+00           
        104  traj.phases.phase0.indep_states.states:phi_15                          c     0.000000E+00     7.756572E-01     1.553343E+00           
        105  traj.phases.phase0.indep_states.states:phi_16                          c     0.000000E+00     8.333108E-01     1.553343E+00           
        106  traj.phases.phase0.indep_states.states:phi_17                          c     0.000000E+00     8.509988E-01     1.553343E+00           
        107  traj.phases.phase0.indep_states.states:phi_18                          c     0.000000E+00     8.903156E-01     1.553343E+00           
        108  traj.phases.phase0.indep_states.states:phi_19                          c     0.000000E+00     9.417573E-01     1.553343E+00           
        109  traj.phases.phase0.indep_states.states:phi_20                          c     0.000000E+00     9.573347E-01     1.553343E+00           
        110  traj.phases.phase0.indep_states.states:phi_21                          c     0.000000E+00     9.918324E-01     1.553343E+00           
        111  traj.phases.phase0.indep_states.states:phi_22                          c     0.000000E+00     1.036714E+00     1.553343E+00           
        112  traj.phases.phase0.indep_states.states:phi_23                          c     0.000000E+00     1.050258E+00     1.553343E+00           
        113  traj.phases.phase0.indep_states.states:phi_24                          c     0.000000E+00     1.079938E+00     1.553343E+00           
        114  traj.phases.phase0.indep_states.states:phi_25                          c     0.000000E+00     1.117782E+00     1.553343E+00           
        115  traj.phases.phase0.indep_states.states:phi_26                          c     0.000000E+00     1.128992E+00     1.553343E+00           
        116  traj.phases.phase0.indep_states.states:phi_27                          c     0.000000E+00     1.153368E+00     1.553343E+00           
        117  traj.phases.phase0.indep_states.states:phi_28                          c     0.000000E+00     1.184034E+00     1.553343E+00           
        118  traj.phases.phase0.indep_states.states:phi_29                          c     0.000000E+00     1.193023E+00     1.553343E+00           
        119  traj.phases.phase0.indep_states.states:phi_30                          c     0.000000E+00     1.212246E+00     1.553343E+00           
        120  traj.phases.phase0.indep_states.states:phi_31                          c     0.000000E+00     1.235684E+00     1.553343E+00           
        121  traj.phases.phase0.indep_states.states:phi_32                          c     0.000000E+00     1.242362E+00     1.553343E+00           
        122  traj.phases.phase0.indep_states.states:phi_33                          c     0.000000E+00     1.256368E+00     1.553343E+00           
        123  traj.phases.phase0.indep_states.states:phi_34                          c     0.000000E+00     1.272808E+00     1.553343E+00           
        124  traj.phases.phase0.indep_states.states:phi_35                          c     0.000000E+00     1.277333E+00     1.553343E+00           
        125  traj.phases.phase0.indep_states.states:phi_36                          c     0.000000E+00     1.286527E+00     1.553343E+00           
        126  traj.phases.phase0.indep_states.states:phi_37                          c     0.000000E+00     1.296695E+00     1.553343E+00           
        127  traj.phases.phase0.indep_states.states:phi_38                          c     0.000000E+00     1.299341E+00     1.553343E+00           
        128  traj.phases.phase0.indep_states.states:phi_39                          c     0.000000E+00     1.304442E+00     1.553343E+00           
        129  traj.phases.phase0.indep_states.states:phi_40                          c     0.000000E+00     1.309551E+00     1.553343E+00           
        130  traj.phases.phase0.indep_states.states:phi_41                          c     0.000000E+00     1.310766E+00     1.553343E+00           
        131  traj.phases.phase0.indep_states.states:phi_42                          c     0.000000E+00     1.312931E+00     1.553343E+00           
        132  traj.phases.phase0.indep_states.states:phi_43                          c     0.000000E+00     1.314826E+00     1.553343E+00           
        133  traj.phases.phase0.indep_states.states:phi_44                          c     0.000000E+00     1.315244E+00     1.553343E+00           
        134  traj.phases.phase0.indep_states.states:psi_0                           c     0.000000E+00     1.565677E+00     1.570796E+00           
        135  traj.phases.phase0.indep_states.states:psi_1                           c     0.000000E+00     1.545947E+00     1.570796E+00           
        136  traj.phases.phase0.indep_states.states:psi_2                           c     0.000000E+00     1.534784E+00     1.570796E+00           
        137  traj.phases.phase0.indep_states.states:psi_3                           c     0.000000E+00     1.500309E+00     1.570796E+00           
        138  traj.phases.phase0.indep_states.states:psi_4                           c     0.000000E+00     1.449337E+00     1.570796E+00           
        139  traj.phases.phase0.indep_states.states:psi_5                           c     0.000000E+00     1.436793E+00     1.570796E+00           
        140  traj.phases.phase0.indep_states.states:psi_6                           c     0.000000E+00     1.414004E+00     1.570796E+00           
        141  traj.phases.phase0.indep_states.states:psi_7                           c     0.000000E+00     1.390797E+00     1.570796E+00           
        142  traj.phases.phase0.indep_states.states:psi_8                           c     0.000000E+00     1.383889E+00     1.570796E+00           
        143  traj.phases.phase0.indep_states.states:psi_9                           c     0.000000E+00     1.365839E+00     1.570796E+00           
        144  traj.phases.phase0.indep_states.states:psi_10                          c     0.000000E+00     1.331827E+00     1.570796E+00           
        145  traj.phases.phase0.indep_states.states:psi_11                          c     0.000000E+00     1.317907E+00     1.570796E+00           
        146  traj.phases.phase0.indep_states.states:psi_12                          c     0.000000E+00     1.284180E+00     1.570796E+00           
        147  traj.phases.phase0.indep_states.states:psi_13                          c     0.000000E+00     1.238868E+00     1.570796E+00           
        148  traj.phases.phase0.indep_states.states:psi_14                          c     0.000000E+00     1.226240E+00     1.570796E+00           
        149  traj.phases.phase0.indep_states.states:psi_15                          c     0.000000E+00     1.198115E+00     1.570796E+00           
        150  traj.phases.phase0.indep_states.states:psi_16                          c     0.000000E+00     1.157920E+00     1.570796E+00           
        151  traj.phases.phase0.indep_states.states:psi_17                          c     0.000000E+00     1.143882E+00     1.570796E+00           
        152  traj.phases.phase0.indep_states.states:psi_18                          c     0.000000E+00     1.109239E+00     1.570796E+00           
        153  traj.phases.phase0.indep_states.states:psi_19                          c     0.000000E+00     1.059639E+00     1.570796E+00           
        154  traj.phases.phase0.indep_states.states:psi_20                          c     0.000000E+00     1.044468E+00     1.570796E+00           
        155  traj.phases.phase0.indep_states.states:psi_21                          c     0.000000E+00     1.011038E+00     1.570796E+00           
        156  traj.phases.phase0.indep_states.states:psi_22                          c     0.000000E+00     9.642348E-01     1.570796E+00           
        157  traj.phases.phase0.indep_states.states:psi_23                          c     0.000000E+00     9.484203E-01     1.570796E+00           
        158  traj.phases.phase0.indep_states.states:psi_24                          c     0.000000E+00     9.097274E-01     1.570796E+00           
        159  traj.phases.phase0.indep_states.states:psi_25                          c     0.000000E+00     8.543942E-01     1.570796E+00           
        160  traj.phases.phase0.indep_states.states:psi_26                          c     0.000000E+00     8.372480E-01     1.570796E+00           
        161  traj.phases.phase0.indep_states.states:psi_27                          c     0.000000E+00     7.989784E-01     1.570796E+00           
        162  traj.phases.phase0.indep_states.states:psi_28                          c     0.000000E+00     7.453301E-01     1.570796E+00           
        163  traj.phases.phase0.indep_states.states:psi_29                          c     0.000000E+00     7.274812E-01     1.570796E+00           
        164  traj.phases.phase0.indep_states.states:psi_30                          c     0.000000E+00     6.849991E-01     1.570796E+00           
        165  traj.phases.phase0.indep_states.states:psi_31                          c     0.000000E+00     6.246440E-01     1.570796E+00           
        166  traj.phases.phase0.indep_states.states:psi_32                          c     0.000000E+00     6.055132E-01     1.570796E+00           
        167  traj.phases.phase0.indep_states.states:psi_33                          c     0.000000E+00     5.612033E-01     1.570796E+00           
        168  traj.phases.phase0.indep_states.states:psi_34                          c     0.000000E+00     4.988996E-01     1.570796E+00           
        169  traj.phases.phase0.indep_states.states:psi_35                          c     0.000000E+00     4.789241E-01     1.570796E+00           
        170  traj.phases.phase0.indep_states.states:psi_36                          c     0.000000E+00     4.332198E-01     1.570796E+00           
        171  traj.phases.phase0.indep_states.states:psi_37                          c     0.000000E+00     3.693556E-01     1.570796E+00           
        172  traj.phases.phase0.indep_states.states:psi_38                          c     0.000000E+00     3.488099E-01     1.570796E+00           
        173  traj.phases.phase0.indep_states.states:psi_39                          c     0.000000E+00     3.020659E-01     1.570796E+00           
        174  traj.phases.phase0.indep_states.states:psi_40                          c     0.000000E+00     2.397120E-01     1.570796E+00           
        175  traj.phases.phase0.indep_states.states:psi_41                          c     0.000000E+00     2.207602E-01     1.570796E+00           
        176  traj.phases.phase0.indep_states.states:psi_42                          c     0.000000E+00     1.786130E-01     1.570796E+00           
        177  traj.phases.phase0.indep_states.states:psi_43                          c     0.000000E+00     1.372196E-01     1.570796E+00           
        178  traj.phases.phase0.indep_states.states:psi_44                          c     0.000000E+00     1.318034E-01     1.570796E+00           
        179  traj.phases.phase0.indep_states.states:theta_0                         c    -1.553343E+00     1.107114E-04     1.553343E+00           
        180  traj.phases.phase0.indep_states.states:theta_1                         c    -1.553343E+00     1.194594E-03     1.553343E+00           
        181  traj.phases.phase0.indep_states.states:theta_2                         c    -1.553343E+00     1.924863E-03     1.553343E+00           
        182  traj.phases.phase0.indep_states.states:theta_3                         c    -1.553343E+00     4.900689E-03     1.553343E+00           
        183  traj.phases.phase0.indep_states.states:theta_4                         c    -1.553343E+00     1.211107E-02     1.553343E+00           
        184  traj.phases.phase0.indep_states.states:theta_5                         c    -1.553343E+00     1.515153E-02     1.553343E+00           
        185  traj.phases.phase0.indep_states.states:theta_6                         c    -1.553343E+00     2.287965E-02     1.553343E+00           
        186  traj.phases.phase0.indep_states.states:theta_7                         c    -1.553343E+00     3.506206E-02     1.553343E+00           
        187  traj.phases.phase0.indep_states.states:theta_8                         c    -1.553343E+00     3.918594E-02     1.553343E+00           
        188  traj.phases.phase0.indep_states.states:theta_9                         c    -1.553343E+00     4.920101E-02     1.553343E+00           
        189  traj.phases.phase0.indep_states.states:theta_10                        c    -1.553343E+00     6.453759E-02     1.553343E+00           
        190  traj.phases.phase0.indep_states.states:theta_11                        c    -1.553343E+00     6.983411E-02     1.553343E+00           
        191  traj.phases.phase0.indep_states.states:theta_12                        c    -1.553343E+00     8.291673E-02     1.553343E+00           
        192  traj.phases.phase0.indep_states.states:theta_13                        c    -1.553343E+00     1.029698E-01     1.553343E+00           
        193  traj.phases.phase0.indep_states.states:theta_14                        c    -1.553343E+00     1.097552E-01     1.553343E+00           
        194  traj.phases.phase0.indep_states.states:theta_15                        c    -1.553343E+00     1.259051E-01     1.553343E+00           
        195  traj.phases.phase0.indep_states.states:theta_16                        c    -1.553343E+00     1.495482E-01     1.553343E+00           
        196  traj.phases.phase0.indep_states.states:theta_17                        c    -1.553343E+00     1.573419E-01     1.553343E+00           
        197  traj.phases.phase0.indep_states.states:theta_18                        c    -1.553343E+00     1.757888E-01     1.553343E+00           
        198  traj.phases.phase0.indep_states.states:theta_19                        c    -1.553343E+00     2.024781E-01     1.553343E+00           
        199  traj.phases.phase0.indep_states.states:theta_20                        c    -1.553343E+00     2.111914E-01     1.553343E+00           
        200  traj.phases.phase0.indep_states.states:theta_21                        c    -1.553343E+00     2.315001E-01     1.553343E+00           
        201  traj.phases.phase0.indep_states.states:theta_22                        c    -1.553343E+00     2.602029E-01     1.553343E+00           
        202  traj.phases.phase0.indep_states.states:theta_23                        c    -1.553343E+00     2.694173E-01     1.553343E+00           
        203  traj.phases.phase0.indep_states.states:theta_24                        c    -1.553343E+00     2.907218E-01     1.553343E+00           
        204  traj.phases.phase0.indep_states.states:theta_25                        c    -1.553343E+00     3.204039E-01     1.553343E+00           
        205  traj.phases.phase0.indep_states.states:theta_26                        c    -1.553343E+00     3.298232E-01     1.553343E+00           
        206  traj.phases.phase0.indep_states.states:theta_27                        c    -1.553343E+00     3.513354E-01     1.553343E+00           
        207  traj.phases.phase0.indep_states.states:theta_28                        c    -1.553343E+00     3.807161E-01     1.553343E+00           
        208  traj.phases.phase0.indep_states.states:theta_29                        c    -1.553343E+00     3.898995E-01     1.553343E+00           
        209  traj.phases.phase0.indep_states.states:theta_30                        c    -1.553343E+00     4.106425E-01     1.553343E+00           
        210  traj.phases.phase0.indep_states.states:theta_31                        c    -1.553343E+00     4.384231E-01     1.553343E+00           
        211  traj.phases.phase0.indep_states.states:theta_32                        c    -1.553343E+00     4.469675E-01     1.553343E+00           
        212  traj.phases.phase0.indep_states.states:theta_33                        c    -1.553343E+00     4.660055E-01     1.553343E+00           
        213  traj.phases.phase0.indep_states.states:theta_34                        c    -1.553343E+00     4.908738E-01     1.553343E+00           
        214  traj.phases.phase0.indep_states.states:theta_35                        c    -1.553343E+00     4.983601E-01     1.553343E+00           
        215  traj.phases.phase0.indep_states.states:theta_36                        c    -1.553343E+00     5.147351E-01     1.553343E+00           
        216  traj.phases.phase0.indep_states.states:theta_37                        c    -1.553343E+00     5.354228E-01     1.553343E+00           
        217  traj.phases.phase0.indep_states.states:theta_38                        c    -1.553343E+00     5.414731E-01     1.553343E+00           
        218  traj.phases.phase0.indep_states.states:theta_39                        c    -1.553343E+00     5.543629E-01     1.553343E+00           
        219  traj.phases.phase0.indep_states.states:theta_40                        c    -1.553343E+00     5.698879E-01     1.553343E+00           
        220  traj.phases.phase0.indep_states.states:theta_41                        c    -1.553343E+00     5.742441E-01     1.553343E+00           
        221  traj.phases.phase0.indep_states.states:theta_42                        c    -1.553343E+00     5.832017E-01     1.553343E+00           
        222  traj.phases.phase0.indep_states.states:theta_43                        c    -1.553343E+00     5.931773E-01     1.553343E+00           
        223  traj.phases.phase0.indep_states.states:theta_44                        c    -1.553343E+00     5.957515E-01     1.553343E+00           
        224  traj.phases.phase0.indep_states.states:v_0                             c    -1.111111E-01     1.024613E+00     4.444444E+16           
        225  traj.phases.phase0.indep_states.states:v_1                             c    -1.111111E-01     1.013619E+00     4.444444E+16           
        226  traj.phases.phase0.indep_states.states:v_2                             c    -1.111111E-01     1.006953E+00     4.444444E+16           
        227  traj.phases.phase0.indep_states.states:v_3                             c    -1.111111E-01     9.859701E-01     4.444444E+16           
        228  traj.phases.phase0.indep_states.states:v_4                             c    -1.111111E-01     9.545005E-01     4.444444E+16           
        229  traj.phases.phase0.indep_states.states:v_5                             c    -1.111111E-01     9.466732E-01     4.444444E+16           
        230  traj.phases.phase0.indep_states.states:v_6                             c    -1.111111E-01     9.322174E-01     4.444444E+16           
        231  traj.phases.phase0.indep_states.states:v_7                             c    -1.111111E-01     9.170874E-01     4.444444E+16           
        232  traj.phases.phase0.indep_states.states:v_8                             c    -1.111111E-01     9.125332E-01     4.444444E+16           
        233  traj.phases.phase0.indep_states.states:v_9                             c    -1.111111E-01     9.005311E-01     4.444444E+16           
        234  traj.phases.phase0.indep_states.states:v_10                            c    -1.111111E-01     8.778435E-01     4.444444E+16           
        235  traj.phases.phase0.indep_states.states:v_11                            c    -1.111111E-01     8.685784E-01     4.444444E+16           
        236  traj.phases.phase0.indep_states.states:v_12                            c    -1.111111E-01     8.461642E-01     4.444444E+16           
        237  traj.phases.phase0.indep_states.states:v_13                            c    -1.111111E-01     8.155658E-01     4.444444E+16           
        238  traj.phases.phase0.indep_states.states:v_14                            c    -1.111111E-01     8.067681E-01     4.444444E+16           
        239  traj.phases.phase0.indep_states.states:v_15                            c    -1.111111E-01     7.868175E-01     4.444444E+16           
        240  traj.phases.phase0.indep_states.states:v_16                            c    -1.111111E-01     7.579006E-01     4.444444E+16           
        241  traj.phases.phase0.indep_states.states:v_17                            c    -1.111111E-01     7.478491E-01     4.444444E+16           
        242  traj.phases.phase0.indep_states.states:v_18                            c    -1.111111E-01     7.231422E-01     4.444444E+16           
        243  traj.phases.phase0.indep_states.states:v_19                            c    -1.111111E-01     6.874418E-01     4.444444E+16           
        244  traj.phases.phase0.indep_states.states:v_20                            c    -1.111111E-01     6.763050E-01     4.444444E+16           
        245  traj.phases.phase0.indep_states.states:v_21                            c    -1.111111E-01     6.513699E-01     4.444444E+16           
        246  traj.phases.phase0.indep_states.states:v_22                            c    -1.111111E-01     6.162967E-01     4.444444E+16           
        247  traj.phases.phase0.indep_states.states:v_23                            c    -1.111111E-01     6.045945E-01     4.444444E+16           
        248  traj.phases.phase0.indep_states.states:v_24                            c    -1.111111E-01     5.763311E-01     4.444444E+16           
        249  traj.phases.phase0.indep_states.states:v_25                            c    -1.111111E-01     5.359749E-01     4.444444E+16           
        250  traj.phases.phase0.indep_states.states:v_26                            c    -1.111111E-01     5.233094E-01     4.444444E+16           
        251  traj.phases.phase0.indep_states.states:v_27                            c    -1.111111E-01     4.946825E-01     4.444444E+16           
        252  traj.phases.phase0.indep_states.states:v_28                            c    -1.111111E-01     4.545387E-01     4.444444E+16           
        253  traj.phases.phase0.indep_states.states:v_29                            c    -1.111111E-01     4.413756E-01     4.444444E+16           
        254  traj.phases.phase0.indep_states.states:v_30                            c    -1.111111E-01     4.105269E-01     4.444444E+16           
        255  traj.phases.phase0.indep_states.states:v_31                            c    -1.111111E-01     3.673682E-01     4.444444E+16           
        256  traj.phases.phase0.indep_states.states:v_32                            c    -1.111111E-01     3.537530E-01     4.444444E+16           
        257  traj.phases.phase0.indep_states.states:v_33                            c    -1.111111E-01     3.222556E-01     4.444444E+16           
        258  traj.phases.phase0.indep_states.states:v_34                            c    -1.111111E-01     2.780734E-01     4.444444E+16           
        259  traj.phases.phase0.indep_states.states:v_35                            c    -1.111111E-01     2.639430E-01     4.444444E+16           
        260  traj.phases.phase0.indep_states.states:v_36                            c    -1.111111E-01     2.317335E-01     4.444444E+16           
        261  traj.phases.phase0.indep_states.states:v_37                            c    -1.111111E-01     1.870633E-01     4.444444E+16           
        262  traj.phases.phase0.indep_states.states:v_38                            c    -1.111111E-01     1.727743E-01     4.444444E+16           
        263  traj.phases.phase0.indep_states.states:v_39                            c    -1.111111E-01     1.403213E-01     4.444444E+16           
        264  traj.phases.phase0.indep_states.states:v_40                            c    -1.111111E-01     9.707601E-02     4.444444E+16           
        265  traj.phases.phase0.indep_states.states:v_41                            c    -1.111111E-01     8.390724E-02     4.444444E+16           
        266  traj.phases.phase0.indep_states.states:v_42                            c    -1.111111E-01     5.349355E-02     4.444444E+16           
        267  traj.phases.phase0.indep_states.states:v_43                            c    -1.111111E-01     1.241642E-02     4.444444E+16           
        268  traj.phases.phase0.control_group.indep_controls.controls:alpha_0       c    -1.570796E+00     3.040729E-01     1.570796E+00           
        269  traj.phases.phase0.control_group.indep_controls.controls:alpha_1       c    -1.570796E+00     3.050556E-01     1.570796E+00           
        270  traj.phases.phase0.control_group.indep_controls.controls:alpha_2       c    -1.570796E+00     3.054886E-01     1.570796E+00           
        271  traj.phases.phase0.control_group.indep_controls.controls:alpha_3       c    -1.570796E+00     3.054027E-01     1.570796E+00           
        272  traj.phases.phase0.control_group.indep_controls.controls:alpha_4       c    -1.570796E+00     3.046790E-01     1.570796E+00           
        273  traj.phases.phase0.control_group.indep_controls.controls:alpha_5       c    -1.570796E+00     3.023534E-01     1.570796E+00           
        274  traj.phases.phase0.control_group.indep_controls.controls:alpha_6       c    -1.570796E+00     3.012967E-01     1.570796E+00           
        275  traj.phases.phase0.control_group.indep_controls.controls:alpha_7       c    -1.570796E+00     3.000026E-01     1.570796E+00           
        276  traj.phases.phase0.control_group.indep_controls.controls:alpha_8       c    -1.570796E+00     3.024928E-01     1.570796E+00           
        277  traj.phases.phase0.control_group.indep_controls.controls:alpha_9       c    -1.570796E+00     3.043139E-01     1.570796E+00           
        278  traj.phases.phase0.control_group.indep_controls.controls:alpha_10      c    -1.570796E+00     3.075127E-01     1.570796E+00           
        279  traj.phases.phase0.control_group.indep_controls.controls:alpha_11      c    -1.570796E+00     3.068697E-01     1.570796E+00           
        280  traj.phases.phase0.control_group.indep_controls.controls:alpha_12      c    -1.570796E+00     3.054445E-01     1.570796E+00           
        281  traj.phases.phase0.control_group.indep_controls.controls:alpha_13      c    -1.570796E+00     3.026548E-01     1.570796E+00           
        282  traj.phases.phase0.control_group.indep_controls.controls:alpha_14      c    -1.570796E+00     3.025687E-01     1.570796E+00           
        283  traj.phases.phase0.control_group.indep_controls.controls:alpha_15      c    -1.570796E+00     3.034506E-01     1.570796E+00           
        284  traj.phases.phase0.control_group.indep_controls.controls:alpha_16      c    -1.570796E+00     3.051818E-01     1.570796E+00           
        285  traj.phases.phase0.control_group.indep_controls.controls:alpha_17      c    -1.570796E+00     3.049804E-01     1.570796E+00           
        286  traj.phases.phase0.control_group.indep_controls.controls:alpha_18      c    -1.570796E+00     3.042910E-01     1.570796E+00           
        287  traj.phases.phase0.control_group.indep_controls.controls:alpha_19      c    -1.570796E+00     3.031232E-01     1.570796E+00           
        288  traj.phases.phase0.control_group.indep_controls.controls:alpha_20      c    -1.570796E+00     3.039923E-01     1.570796E+00           
        289  traj.phases.phase0.control_group.indep_controls.controls:alpha_21      c    -1.570796E+00     3.048667E-01     1.570796E+00           
        290  traj.phases.phase0.control_group.indep_controls.controls:alpha_22      c    -1.570796E+00     3.062196E-01     1.570796E+00           
        291  traj.phases.phase0.control_group.indep_controls.controls:alpha_23      c    -1.570796E+00     3.048712E-01     1.570796E+00           
        292  traj.phases.phase0.control_group.indep_controls.controls:alpha_24      c    -1.570796E+00     3.036677E-01     1.570796E+00           
        293  traj.phases.phase0.control_group.indep_controls.controls:alpha_25      c    -1.570796E+00     3.016662E-01     1.570796E+00           
        294  traj.phases.phase0.control_group.indep_controls.controls:alpha_26      c    -1.570796E+00     3.027852E-01     1.570796E+00           
        295  traj.phases.phase0.control_group.indep_controls.controls:alpha_27      c    -1.570796E+00     3.040769E-01     1.570796E+00           
        296  traj.phases.phase0.control_group.indep_controls.controls:alpha_28      c    -1.570796E+00     3.064674E-01     1.570796E+00           
        297  traj.phases.phase0.control_group.indep_controls.controls:alpha_29      c    -1.570796E+00     3.062083E-01     1.570796E+00           
        298  traj.phases.phase0.control_group.indep_controls.controls:alpha_30      c    -1.570796E+00     3.052668E-01     1.570796E+00           
        299  traj.phases.phase0.control_group.indep_controls.controls:alpha_31      c    -1.570796E+00     3.032609E-01     1.570796E+00           
        300  traj.phases.phase0.control_group.indep_controls.controls:alpha_32      c    -1.570796E+00     3.025385E-01     1.570796E+00           
        301  traj.phases.phase0.control_group.indep_controls.controls:alpha_33      c    -1.570796E+00     3.028041E-01     1.570796E+00           
        302  traj.phases.phase0.control_group.indep_controls.controls:alpha_34      c    -1.570796E+00     3.034910E-01     1.570796E+00           
        303  traj.phases.phase0.control_group.indep_controls.controls:alpha_35      c    -1.570796E+00     3.038045E-01     1.570796E+00           
        304  traj.phases.phase0.control_group.indep_controls.controls:alpha_36      c    -1.570796E+00     3.037505E-01     1.570796E+00           
        305  traj.phases.phase0.control_group.indep_controls.controls:alpha_37      c    -1.570796E+00     3.040400E-01     1.570796E+00           
        306  traj.phases.phase0.control_group.indep_controls.controls:alpha_38      c    -1.570796E+00     3.060731E-01     1.570796E+00           
        307  traj.phases.phase0.control_group.indep_controls.controls:alpha_39      c    -1.570796E+00     3.071112E-01     1.570796E+00           
        308  traj.phases.phase0.control_group.indep_controls.controls:alpha_40      c    -1.570796E+00     3.073653E-01     1.570796E+00           
        309  traj.phases.phase0.control_group.indep_controls.controls:alpha_41      c    -1.570796E+00     3.000310E-01     1.570796E+00           
        310  traj.phases.phase0.control_group.indep_controls.controls:alpha_42      c    -1.570796E+00     2.958531E-01     1.570796E+00           
        311  traj.phases.phase0.control_group.indep_controls.controls:alpha_43      c    -1.570796E+00     2.875561E-01     1.570796E+00           
        312  traj.phases.phase0.control_group.indep_controls.controls:alpha_44      c    -1.570796E+00     2.836335E-01     1.570796E+00           
        313  traj.phases.phase0.control_group.indep_controls.controls:beta_0        c    -1.553343E+00    -1.302729E+00     1.745329E-02           
        314  traj.phases.phase0.control_group.indep_controls.controls:beta_1        c    -1.553343E+00    -1.275652E+00     1.745329E-02           
        315  traj.phases.phase0.control_group.indep_controls.controls:beta_2        c    -1.553343E+00    -1.251509E+00     1.745329E-02           
        316  traj.phases.phase0.control_group.indep_controls.controls:beta_3        c    -1.553343E+00    -1.247061E+00     1.745329E-02           
        317  traj.phases.phase0.control_group.indep_controls.controls:beta_4        c    -1.553343E+00    -1.239116E+00     1.745329E-02           
        318  traj.phases.phase0.control_group.indep_controls.controls:beta_5        c    -1.553343E+00    -1.229736E+00     1.745329E-02           
        319  traj.phases.phase0.control_group.indep_controls.controls:beta_6        c    -1.553343E+00    -1.227149E+00     1.745329E-02           
        320  traj.phases.phase0.control_group.indep_controls.controls:beta_7        c    -1.553343E+00    -1.209604E+00     1.745329E-02           
        321  traj.phases.phase0.control_group.indep_controls.controls:beta_8        c    -1.553343E+00    -1.146537E+00     1.745329E-02           
        322  traj.phases.phase0.control_group.indep_controls.controls:beta_9        c    -1.553343E+00    -1.117190E+00     1.745329E-02           
        323  traj.phases.phase0.control_group.indep_controls.controls:beta_10       c    -1.553343E+00    -1.057375E+00     1.745329E-02           
        324  traj.phases.phase0.control_group.indep_controls.controls:beta_11       c    -1.553343E+00    -1.016068E+00     1.745329E-02           
        325  traj.phases.phase0.control_group.indep_controls.controls:beta_12       c    -1.553343E+00    -1.012954E+00     1.745329E-02           
        326  traj.phases.phase0.control_group.indep_controls.controls:beta_13       c    -1.553343E+00    -1.003222E+00     1.745329E-02           
        327  traj.phases.phase0.control_group.indep_controls.controls:beta_14       c    -1.553343E+00    -9.632470E-01     1.745329E-02           
        328  traj.phases.phase0.control_group.indep_controls.controls:beta_15       c    -1.553343E+00    -9.441821E-01     1.745329E-02           
        329  traj.phases.phase0.control_group.indep_controls.controls:beta_16       c    -1.553343E+00    -9.010388E-01     1.745329E-02           
        330  traj.phases.phase0.control_group.indep_controls.controls:beta_17       c    -1.553343E+00    -8.547883E-01     1.745329E-02           
        331  traj.phases.phase0.control_group.indep_controls.controls:beta_18       c    -1.553343E+00    -8.433581E-01     1.745329E-02           
        332  traj.phases.phase0.control_group.indep_controls.controls:beta_19       c    -1.553343E+00    -8.163751E-01     1.745329E-02           
        333  traj.phases.phase0.control_group.indep_controls.controls:beta_20       c    -1.553343E+00    -7.706893E-01     1.745329E-02           
        334  traj.phases.phase0.control_group.indep_controls.controls:beta_21       c    -1.553343E+00    -7.541874E-01     1.745329E-02           
        335  traj.phases.phase0.control_group.indep_controls.controls:beta_22       c    -1.553343E+00    -7.180935E-01     1.745329E-02           
        336  traj.phases.phase0.control_group.indep_controls.controls:beta_23       c    -1.553343E+00    -6.775451E-01     1.745329E-02           
        337  traj.phases.phase0.control_group.indep_controls.controls:beta_24       c    -1.553343E+00    -6.669472E-01     1.745329E-02           
        338  traj.phases.phase0.control_group.indep_controls.controls:beta_25       c    -1.553343E+00    -6.406154E-01     1.745329E-02           
        339  traj.phases.phase0.control_group.indep_controls.controls:beta_26       c    -1.553343E+00    -5.934649E-01     1.745329E-02           
        340  traj.phases.phase0.control_group.indep_controls.controls:beta_27       c    -1.553343E+00    -5.759285E-01     1.745329E-02           
        341  traj.phases.phase0.control_group.indep_controls.controls:beta_28       c    -1.553343E+00    -5.374644E-01     1.745329E-02           
        342  traj.phases.phase0.control_group.indep_controls.controls:beta_29       c    -1.553343E+00    -4.946732E-01     1.745329E-02           
        343  traj.phases.phase0.control_group.indep_controls.controls:beta_30       c    -1.553343E+00    -4.836137E-01     1.745329E-02           
        344  traj.phases.phase0.control_group.indep_controls.controls:beta_31       c    -1.553343E+00    -4.577359E-01     1.745329E-02           
        345  traj.phases.phase0.control_group.indep_controls.controls:beta_32       c    -1.553343E+00    -4.157245E-01     1.745329E-02           
        346  traj.phases.phase0.control_group.indep_controls.controls:beta_33       c    -1.553343E+00    -4.009049E-01     1.745329E-02           
        347  traj.phases.phase0.control_group.indep_controls.controls:beta_34       c    -1.553343E+00    -3.667959E-01     1.745329E-02           
        348  traj.phases.phase0.control_group.indep_controls.controls:beta_35       c    -1.553343E+00    -3.219163E-01     1.745329E-02           
        349  traj.phases.phase0.control_group.indep_controls.controls:beta_36       c    -1.553343E+00    -3.082396E-01     1.745329E-02           
        350  traj.phases.phase0.control_group.indep_controls.controls:beta_37       c    -1.553343E+00    -2.775231E-01     1.745329E-02           
        351  traj.phases.phase0.control_group.indep_controls.controls:beta_38       c    -1.553343E+00    -2.361624E-01     1.745329E-02           
        352  traj.phases.phase0.control_group.indep_controls.controls:beta_39       c    -1.553343E+00    -2.233188E-01     1.745329E-02           
        353  traj.phases.phase0.control_group.indep_controls.controls:beta_40       c    -1.553343E+00    -1.937905E-01     1.745329E-02           
        354  traj.phases.phase0.control_group.indep_controls.controls:beta_41       c    -1.553343E+00    -1.522144E-01     1.745329E-02           
        355  traj.phases.phase0.control_group.indep_controls.controls:beta_42       c    -1.553343E+00    -1.388545E-01     1.745329E-02           
        356  traj.phases.phase0.control_group.indep_controls.controls:beta_43       c    -1.553343E+00    -1.027161E-01     1.745329E-02           
        357  traj.phases.phase0.control_group.indep_controls.controls:beta_44       c    -1.553343E+00    -3.500662E-02     1.745329E-02           

   Constraints (i - inequality, e - equality)
      Index  Name                                                               Type          Lower           Value           Upper    Status  Lagrange Multiplier (N/A)
          0  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.750364E-13    0.000000E+00              9.00000E+100
          1  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -6.420767E-09    0.000000E+00              9.00000E+100
          2  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.310823E-08    0.000000E+00              9.00000E+100
          3  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.338110E-08    0.000000E+00              9.00000E+100
          4  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -6.333795E-09    0.000000E+00              9.00000E+100
          5  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.070980E-08    0.000000E+00              9.00000E+100
          6  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.341048E-08    0.000000E+00              9.00000E+100
          7  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.209714E-08    0.000000E+00              9.00000E+100
          8  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -3.622801E-11    0.000000E+00              9.00000E+100
          9  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -4.651672E-09    0.000000E+00              9.00000E+100
         10  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.424184E-08    0.000000E+00              9.00000E+100
         11  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -8.740558E-09    0.000000E+00              9.00000E+100
         12  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.631927E-09    0.000000E+00              9.00000E+100
         13  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    3.430305E-08    0.000000E+00              9.00000E+100
         14  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    3.848498E-08    0.000000E+00              9.00000E+100
         15  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.029131E-08    0.000000E+00              9.00000E+100
         16  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.860993E-08    0.000000E+00              9.00000E+100
         17  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -3.491208E-08    0.000000E+00              9.00000E+100
         18  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -2.699596E-08    0.000000E+00              9.00000E+100
         19  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    7.744457E-09    0.000000E+00              9.00000E+100
         20  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    4.077172E-08    0.000000E+00              9.00000E+100
         21  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.845387E-08    0.000000E+00              9.00000E+100
         22  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -6.494643E-09    0.000000E+00              9.00000E+100
         23  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -2.215466E-08    0.000000E+00              9.00000E+100
         24  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.338724E-08    0.000000E+00              9.00000E+100
         25  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    8.504803E-09    0.000000E+00              9.00000E+100
         26  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    9.191277E-09    0.000000E+00              9.00000E+100
         27  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -3.816317E-09    0.000000E+00              9.00000E+100
         28  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.286954E-08    0.000000E+00              9.00000E+100
         29  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.326457E-09    0.000000E+00              9.00000E+100
         30  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    9.418331E-09    0.000000E+00              9.00000E+100
         31  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.822890E-09    0.000000E+00              9.00000E+100
         32  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -8.389856E-09    0.000000E+00              9.00000E+100
         33  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -2.332977E-09    0.000000E+00              9.00000E+100
         34  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.585528E-08    0.000000E+00              9.00000E+100
         35  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.805062E-11    0.000000E+00              9.00000E+100
         36  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.629466E-08    0.000000E+00              9.00000E+100
         37  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.474979E-08    0.000000E+00              9.00000E+100
         38  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.687113E-08    0.000000E+00              9.00000E+100
         39  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    2.621267E-08    0.000000E+00              9.00000E+100
         40  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.492111E-09    0.000000E+00              9.00000E+100
         41  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -1.207928E-08    0.000000E+00              9.00000E+100
         42  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00   -4.799154E-09    0.000000E+00              9.00000E+100
         43  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    4.193199E-09    0.000000E+00              9.00000E+100
         44  traj.phases.phase0.collocation_constraint.defects:h                   e   0.000000E+00    1.312192E-09    0.000000E+00              9.00000E+100
         45  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -2.956392E-11    0.000000E+00              9.00000E+100
         46  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -3.977603E-12    0.000000E+00              9.00000E+100
         47  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    1.813436E-11    0.000000E+00              9.00000E+100
         48  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    4.442054E-12    0.000000E+00              9.00000E+100
         49  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -3.711988E-11    0.000000E+00              9.00000E+100
         50  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -3.429730E-11    0.000000E+00              9.00000E+100
         51  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.904010E-11    0.000000E+00              9.00000E+100
         52  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.303829E-12    0.000000E+00              9.00000E+100
         53  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    1.850287E-12    0.000000E+00              9.00000E+100
         54  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    1.831381E-12    0.000000E+00              9.00000E+100
         55  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -3.641364E-13    0.000000E+00              9.00000E+100
         56  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -7.978212E-11    0.000000E+00              9.00000E+100
         57  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.266808E-10    0.000000E+00              9.00000E+100
         58  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -7.071094E-11    0.000000E+00              9.00000E+100
         59  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    4.756351E-11    0.000000E+00              9.00000E+100
         60  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    8.947996E-12    0.000000E+00              9.00000E+100
         61  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -2.669346E-11    0.000000E+00              9.00000E+100
         62  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -5.789393E-12    0.000000E+00              9.00000E+100
         63  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -7.256594E-11    0.000000E+00              9.00000E+100
         64  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.262380E-10    0.000000E+00              9.00000E+100
         65  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    1.068266E-12    0.000000E+00              9.00000E+100
         66  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.371691E-11    0.000000E+00              9.00000E+100
         67  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -9.713437E-12    0.000000E+00              9.00000E+100
         68  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    4.416730E-12    0.000000E+00              9.00000E+100
         69  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -3.436800E-11    0.000000E+00              9.00000E+100
         70  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.841513E-11    0.000000E+00              9.00000E+100
         71  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -7.937019E-12    0.000000E+00              9.00000E+100
         72  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.096693E-11    0.000000E+00              9.00000E+100
         73  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    2.647124E-11    0.000000E+00              9.00000E+100
         74  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -4.300833E-13    0.000000E+00              9.00000E+100
         75  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    7.491950E-12    0.000000E+00              9.00000E+100
         76  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    2.840755E-12    0.000000E+00              9.00000E+100
         77  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    5.571218E-12    0.000000E+00              9.00000E+100
         78  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -2.551647E-11    0.000000E+00              9.00000E+100
         79  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    1.564987E-11    0.000000E+00              9.00000E+100
         80  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -5.010484E-11    0.000000E+00              9.00000E+100
         81  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -4.878877E-11    0.000000E+00              9.00000E+100
         82  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -7.211062E-12    0.000000E+00              9.00000E+100
         83  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -2.916943E-11    0.000000E+00              9.00000E+100
         84  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    8.882653E-12    0.000000E+00              9.00000E+100
         85  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -9.122941E-11    0.000000E+00              9.00000E+100
         86  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    7.810339E-12    0.000000E+00              9.00000E+100
         87  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -7.758595E-12    0.000000E+00              9.00000E+100
         88  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00    7.947572E-11    0.000000E+00              9.00000E+100
         89  traj.phases.phase0.collocation_constraint.defects:gamma               e   0.000000E+00   -1.934413E-11    0.000000E+00              9.00000E+100
         90  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.451545E-17    0.000000E+00              9.00000E+100
         91  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    9.507620E-14    0.000000E+00              9.00000E+100
         92  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    2.049582E-14    0.000000E+00              9.00000E+100
         93  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.191718E-13    0.000000E+00              9.00000E+100
         94  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -5.963963E-13    0.000000E+00              9.00000E+100
         95  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.057160E-12    0.000000E+00              9.00000E+100
         96  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.141756E-12    0.000000E+00              9.00000E+100
         97  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.295170E-12    0.000000E+00              9.00000E+100
         98  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.436028E-12    0.000000E+00              9.00000E+100
         99  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.460211E-12    0.000000E+00              9.00000E+100
        100  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.474102E-12    0.000000E+00              9.00000E+100
        101  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.579295E-12    0.000000E+00              9.00000E+100
        102  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.662861E-12    0.000000E+00              9.00000E+100
        103  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.169044E-12    0.000000E+00              9.00000E+100
        104  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.538221E-12    0.000000E+00              9.00000E+100
        105  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.812280E-12    0.000000E+00              9.00000E+100
        106  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.407168E-12    0.000000E+00              9.00000E+100
        107  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.318096E-12    0.000000E+00              9.00000E+100
        108  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.503451E-12    0.000000E+00              9.00000E+100
        109  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.598903E-12    0.000000E+00              9.00000E+100
        110  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -4.809702E-12    0.000000E+00              9.00000E+100
        111  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -4.789191E-12    0.000000E+00              9.00000E+100
        112  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.980071E-12    0.000000E+00              9.00000E+100
        113  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.746947E-12    0.000000E+00              9.00000E+100
        114  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.883668E-12    0.000000E+00              9.00000E+100
        115  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.587588E-12    0.000000E+00              9.00000E+100
        116  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -4.008405E-12    0.000000E+00              9.00000E+100
        117  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.605587E-12    0.000000E+00              9.00000E+100
        118  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.740285E-12    0.000000E+00              9.00000E+100
        119  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.108478E-12    0.000000E+00              9.00000E+100
        120  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.149473E-12    0.000000E+00              9.00000E+100
        121  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.078667E-12    0.000000E+00              9.00000E+100
        122  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.255639E-12    0.000000E+00              9.00000E+100
        123  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.499430E-12    0.000000E+00              9.00000E+100
        124  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -2.771892E-12    0.000000E+00              9.00000E+100
        125  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.558393E-12    0.000000E+00              9.00000E+100
        126  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -7.882815E-13    0.000000E+00              9.00000E+100
        127  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.355500E-13    0.000000E+00              9.00000E+100
        128  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -8.748298E-13    0.000000E+00              9.00000E+100
        129  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.033636E-12    0.000000E+00              9.00000E+100
        130  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -5.497164E-13    0.000000E+00              9.00000E+100
        131  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00    6.522880E-16    0.000000E+00              9.00000E+100
        132  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -1.130822E-13    0.000000E+00              9.00000E+100
        133  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.615018E-13    0.000000E+00              9.00000E+100
        134  traj.phases.phase0.collocation_constraint.defects:phi                 e   0.000000E+00   -3.932322E-13    0.000000E+00              9.00000E+100
        135  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -3.127715E-11    0.000000E+00              9.00000E+100
        136  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -2.284129E-11    0.000000E+00              9.00000E+100
        137  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.896556E-11    0.000000E+00              9.00000E+100
        138  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    5.777573E-11    0.000000E+00              9.00000E+100
        139  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    8.010790E-11    0.000000E+00              9.00000E+100
        140  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    6.110542E-11    0.000000E+00              9.00000E+100
        141  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    4.658207E-11    0.000000E+00              9.00000E+100
        142  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.296619E-11    0.000000E+00              9.00000E+100
        143  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    4.888756E-12    0.000000E+00              9.00000E+100
        144  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    4.659474E-12    0.000000E+00              9.00000E+100
        145  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.800213E-11    0.000000E+00              9.00000E+100
        146  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    9.267952E-11    0.000000E+00              9.00000E+100
        147  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.038301E-10    0.000000E+00              9.00000E+100
        148  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -9.639739E-12    0.000000E+00              9.00000E+100
        149  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.330911E-10    0.000000E+00              9.00000E+100
        150  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.629377E-10    0.000000E+00              9.00000E+100
        151  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.495885E-10    0.000000E+00              9.00000E+100
        152  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -6.422419E-12    0.000000E+00              9.00000E+100
        153  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    4.730060E-11    0.000000E+00              9.00000E+100
        154  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.569716E-10    0.000000E+00              9.00000E+100
        155  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -2.034558E-12    0.000000E+00              9.00000E+100
        156  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    4.272276E-11    0.000000E+00              9.00000E+100
        157  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.057118E-10    0.000000E+00              9.00000E+100
        158  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -1.472676E-11    0.000000E+00              9.00000E+100
        159  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    8.174376E-14    0.000000E+00              9.00000E+100
        160  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.416650E-11    0.000000E+00              9.00000E+100
        161  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    6.807477E-12    0.000000E+00              9.00000E+100
        162  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    3.041638E-11    0.000000E+00              9.00000E+100
        163  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    4.585794E-12    0.000000E+00              9.00000E+100
        164  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -2.274789E-11    0.000000E+00              9.00000E+100
        165  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -8.920550E-12    0.000000E+00              9.00000E+100
        166  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -1.407020E-11    0.000000E+00              9.00000E+100
        167  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    5.795243E-12    0.000000E+00              9.00000E+100
        168  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.535124E-11    0.000000E+00              9.00000E+100
        169  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -1.841034E-11    0.000000E+00              9.00000E+100
        170  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    8.234762E-11    0.000000E+00              9.00000E+100
        171  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    5.771773E-11    0.000000E+00              9.00000E+100
        172  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -2.120272E-12    0.000000E+00              9.00000E+100
        173  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.179858E-11    0.000000E+00              9.00000E+100
        174  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -4.515147E-12    0.000000E+00              9.00000E+100
        175  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    2.229445E-11    0.000000E+00              9.00000E+100
        176  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -4.908254E-13    0.000000E+00              9.00000E+100
        177  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00    1.670550E-11    0.000000E+00              9.00000E+100
        178  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -1.671915E-11    0.000000E+00              9.00000E+100
        179  traj.phases.phase0.collocation_constraint.defects:psi                 e   0.000000E+00   -3.764117E-12    0.000000E+00              9.00000E+100
        180  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -1.870904E-19    0.000000E+00              9.00000E+100
        181  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -6.927924E-14    0.000000E+00              9.00000E+100
        182  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    3.604363E-13    0.000000E+00              9.00000E+100
        183  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    7.592651E-13    0.000000E+00              9.00000E+100
        184  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    2.329190E-12    0.000000E+00              9.00000E+100
        185  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    5.311192E-12    0.000000E+00              9.00000E+100
        186  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    6.096955E-12    0.000000E+00              9.00000E+100
        187  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    7.375832E-12    0.000000E+00              9.00000E+100
        188  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    8.271083E-12    0.000000E+00              9.00000E+100
        189  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    8.438016E-12    0.000000E+00              9.00000E+100
        190  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    9.016961E-12    0.000000E+00              9.00000E+100
        191  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.142930E-11    0.000000E+00              9.00000E+100
        192  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.297143E-11    0.000000E+00              9.00000E+100
        193  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.578212E-11    0.000000E+00              9.00000E+100
        194  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.364646E-11    0.000000E+00              9.00000E+100
        195  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.095727E-11    0.000000E+00              9.00000E+100
        196  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    5.564048E-12    0.000000E+00              9.00000E+100
        197  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    2.414768E-12    0.000000E+00              9.00000E+100
        198  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    2.617800E-12    0.000000E+00              9.00000E+100
        199  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    4.813537E-12    0.000000E+00              9.00000E+100
        200  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    7.638073E-12    0.000000E+00              9.00000E+100
        201  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    6.852156E-12    0.000000E+00              9.00000E+100
        202  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    3.972563E-12    0.000000E+00              9.00000E+100
        203  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.569414E-12    0.000000E+00              9.00000E+100
        204  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.559181E-12    0.000000E+00              9.00000E+100
        205  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    2.245932E-12    0.000000E+00              9.00000E+100
        206  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    2.556116E-12    0.000000E+00              9.00000E+100
        207  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.993214E-12    0.000000E+00              9.00000E+100
        208  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    8.195641E-13    0.000000E+00              9.00000E+100
        209  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -2.177426E-13    0.000000E+00              9.00000E+100
        210  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -3.237236E-13    0.000000E+00              9.00000E+100
        211  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -3.196375E-13    0.000000E+00              9.00000E+100
        212  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.166425E-13    0.000000E+00              9.00000E+100
        213  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    2.465050E-13    0.000000E+00              9.00000E+100
        214  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    1.132895E-13    0.000000E+00              9.00000E+100
        215  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -6.966726E-13    0.000000E+00              9.00000E+100
        216  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -6.846938E-13    0.000000E+00              9.00000E+100
        217  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -5.828969E-13    0.000000E+00              9.00000E+100
        218  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -6.979391E-13    0.000000E+00              9.00000E+100
        219  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -6.903439E-13    0.000000E+00              9.00000E+100
        220  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -6.505208E-13    0.000000E+00              9.00000E+100
        221  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    2.043957E-14    0.000000E+00              9.00000E+100
        222  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -8.738119E-14    0.000000E+00              9.00000E+100
        223  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00   -9.217674E-14    0.000000E+00              9.00000E+100
        224  traj.phases.phase0.collocation_constraint.defects:theta               e   0.000000E+00    3.420203E-14    0.000000E+00              9.00000E+100
        225  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    6.277881E-12    0.000000E+00              9.00000E+100
        226  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    7.554923E-13    0.000000E+00              9.00000E+100
        227  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.555025E-11    0.000000E+00              9.00000E+100
        228  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.999129E-11    0.000000E+00              9.00000E+100
        229  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.134634E-11    0.000000E+00              9.00000E+100
        230  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.540127E-11    0.000000E+00              9.00000E+100
        231  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.238388E-11    0.000000E+00              9.00000E+100
        232  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    7.477750E-12    0.000000E+00              9.00000E+100
        233  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.673223E-13    0.000000E+00              9.00000E+100
        234  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.768504E-13    0.000000E+00              9.00000E+100
        235  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.961377E-12    0.000000E+00              9.00000E+100
        236  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.510041E-11    0.000000E+00              9.00000E+100
        237  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.812722E-11    0.000000E+00              9.00000E+100
        238  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.002741E-11    0.000000E+00              9.00000E+100
        239  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.923917E-11    0.000000E+00              9.00000E+100
        240  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.169723E-10    0.000000E+00              9.00000E+100
        241  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.099639E-10    0.000000E+00              9.00000E+100
        242  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.379229E-13    0.000000E+00              9.00000E+100
        243  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.831061E-11    0.000000E+00              9.00000E+100
        244  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    6.424773E-11    0.000000E+00              9.00000E+100
        245  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -3.820720E-12    0.000000E+00              9.00000E+100
        246  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.143937E-11    0.000000E+00              9.00000E+100
        247  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    4.204095E-11    0.000000E+00              9.00000E+100
        248  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -1.235971E-12    0.000000E+00              9.00000E+100
        249  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    6.061014E-12    0.000000E+00              9.00000E+100
        250  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.322732E-12    0.000000E+00              9.00000E+100
        251  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    5.911629E-12    0.000000E+00              9.00000E+100
        252  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.335514E-11    0.000000E+00              9.00000E+100
        253  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.855048E-12    0.000000E+00              9.00000E+100
        254  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -2.394864E-12    0.000000E+00              9.00000E+100
        255  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -3.461953E-12    0.000000E+00              9.00000E+100
        256  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    6.027529E-13    0.000000E+00              9.00000E+100
        257  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -1.907696E-12    0.000000E+00              9.00000E+100
        258  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.316963E-12    0.000000E+00              9.00000E+100
        259  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -4.823997E-12    0.000000E+00              9.00000E+100
        260  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.358212E-11    0.000000E+00              9.00000E+100
        261  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.860388E-11    0.000000E+00              9.00000E+100
        262  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    3.401746E-13    0.000000E+00              9.00000E+100
        263  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -2.420667E-12    0.000000E+00              9.00000E+100
        264  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -2.442742E-12    0.000000E+00              9.00000E+100
        265  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.741911E-11    0.000000E+00              9.00000E+100
        266  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    1.590457E-12    0.000000E+00              9.00000E+100
        267  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    2.194642E-12    0.000000E+00              9.00000E+100
        268  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00   -2.946571E-12    0.000000E+00              9.00000E+100
        269  traj.phases.phase0.collocation_constraint.defects:v                   e   0.000000E+00    7.599003E-13    0.000000E+00              9.00000E+100
        270  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00   -5.551115E-17    0.000000E+00              9.00000E+100
        271  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        272  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        273  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    5.551115E-17    0.000000E+00              9.00000E+100
        274  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        275  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        276  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        277  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        278  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00   -1.110223E-16    0.000000E+00              9.00000E+100
        279  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00   -5.551115E-17    0.000000E+00              9.00000E+100
        280  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        281  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        282  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    1.110223E-16    0.000000E+00              9.00000E+100
        283  traj.phases.phase0.continuity_comp.defect_controls:alpha              e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        284  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -2.497962E-15    0.000000E+00              9.00000E+100
        285  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    4.762882E-17    0.000000E+00              9.00000E+100
        286  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    2.585565E-15    0.000000E+00              9.00000E+100
        287  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -3.334017E-15    0.000000E+00              9.00000E+100
        288  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -8.777311E-16    0.000000E+00              9.00000E+100
        289  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -2.537936E-15    0.000000E+00              9.00000E+100
        290  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    3.327213E-15    0.000000E+00              9.00000E+100
        291  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -8.301023E-16    0.000000E+00              9.00000E+100
        292  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -8.301023E-16    0.000000E+00              9.00000E+100
        293  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    8.369064E-16    0.000000E+00              9.00000E+100
        294  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    7.994838E-16    0.000000E+00              9.00000E+100
        295  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    4.155615E-15    0.000000E+00              9.00000E+100
        296  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00    8.301023E-16    0.000000E+00              9.00000E+100
        297  traj.phases.phase0.continuity_comp.defect_control_rates:alpha_rate    e   0.000000E+00   -5.824324E-15    0.000000E+00              9.00000E+100
        298  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    4.440892E-16    0.000000E+00              9.00000E+100
        299  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    2.220446E-16    0.000000E+00              9.00000E+100
        300  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        301  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    2.220446E-16    0.000000E+00              9.00000E+100
        302  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00   -3.330669E-16    0.000000E+00              9.00000E+100
        303  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00   -2.220446E-16    0.000000E+00              9.00000E+100
        304  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    3.330669E-16    0.000000E+00              9.00000E+100
        305  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        306  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        307  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    5.551115E-17    0.000000E+00              9.00000E+100
        308  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        309  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    1.110223E-16    0.000000E+00              9.00000E+100
        310  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00   -2.775558E-17    0.000000E+00              9.00000E+100
        311  traj.phases.phase0.continuity_comp.defect_controls:beta               e   0.000000E+00    2.775558E-17    0.000000E+00              9.00000E+100
        312  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    1.997689E-14    0.000000E+00              9.00000E+100
        313  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00   -3.429275E-15    0.000000E+00              9.00000E+100
        314  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00   -5.443294E-15    0.000000E+00              9.00000E+100
        315  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    9.995248E-15    0.000000E+00              9.00000E+100
        316  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00   -4.136903E-15    0.000000E+00              9.00000E+100
        317  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    3.701440E-15    0.000000E+00              9.00000E+100
        318  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    6.749684E-15    0.000000E+00              9.00000E+100
        319  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    3.320409E-15    0.000000E+00              9.00000E+100
        320  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        321  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    0.000000E+00    0.000000E+00              9.00000E+100
        322  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    4.354635E-16    0.000000E+00              9.00000E+100
        323  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    1.088659E-15    0.000000E+00              9.00000E+100
        324  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00   -8.709270E-16    0.000000E+00              9.00000E+100
        325  traj.phases.phase0.continuity_comp.defect_control_rates:beta_rate     e   0.000000E+00    8.709270E-16    0.000000E+00              9.00000E+100

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


Simulating trajectory traj
Done simulating trajectory traj

References


  1. J. Betts. Practical Methods for Optimal Control and Estimation Using Nonlinear Programming. Society for Industrial and Applied Mathematics, second edition, 2010. URL: https://epubs.siam.org/doi/abs/10.1137/1.9780898718577, arXiv:https://epubs.siam.org/doi/pdf/10.1137/1.9780898718577, doi:10.1137/1.9780898718577