Timeseries Outputs#
Different optimal control transcriptions work in different ways. The Radau Pseudospectral transcription keeps a contiguous vector of state values at all nodes. The Gauss Lobatto transcription keeps two separate continuous vectors; one at the discretization nodes and the other at the collocation nodes. Retrieving a timeseries values of output values is thus transcription dependent.
In order to make obtaining the timeseries output of a phase easier, each phase provides a timeseries component which collects and outputs the appropriate timeseries data. For the pseudospectral transcriptions, timeseries outputs are provided at all nodes. By default, the timeseries output will include the following variables for every problem.
Paths to timeseries outputs in Dymos#
Path |
Description |
|---|---|
|
Current time value |
|
Current phase elapsed time |
|
Value of state variable named x |
|
Value of control variable named u |
|
Time derivative of control named u |
|
Second time derivative of control named u |
|
Value of polynomial control variable named u |
|
Time derivative of polynomial control named u |
|
Second time derivative of polynomial control named u |
|
Value of parameter named d |
Adding additional timeseries outputs#
In addition to these default values, any output of the ODE can be added to the timeseries output
using the add_timeseries_output method on Phase. These outputs are available as
<phase path>.timeseries.<output name>. A glob pattern can be used with add_timeseries_output
to add multiple outputs to the timeseries simultaneously. For instance, just passing ‘*’ as the variable
name will add all dynamic outputs of the ODE to the timeseries.
Dymos will ignore any ODE outputs that are not sized such that the first dimension is the same as the number of nodes in the ODE. That is, if the output variable doesn’t appear to be dynamic, it will not be included in the timeseries outputs.
- Phase.add_timeseries_output(name, output_name=None, units=unspecified, shape=unspecified, timeseries='timeseries', **kwargs)[source]
Add a variable to the timeseries outputs of the phase.
If name is given as an expression, this expression will be passed to an OpenMDAO ExecComp and the result computed and stored in the timeseries output under the variable name to the left of the equal sign.
- Parameters:
- namestr, or list of str
The name(s) of the variable to be used as a timeseries output, or a mathematical expression to be used as a timeseries output. If a name, it must be one of the integration variable, the phase-relative value of the integration variable (e.g. ‘time_phase’, one of the states, controls, control rates, or parameters, in the phase, the path to an output variable in the ODE, or a glob pattern matching some outputs in the ODE.
- output_namestr or None or list or dict
The name of the variable as listed in the phase timeseries outputs. By default this is the last element in name when split by dots. The user may override the timeseries name if splitting the path causes name collisions.
- unitsstr or None or _unspecified
The units to express the timeseries output. If None, use the units associated with the target. If provided, must be compatible with the target units. If a list of names is provided, units can be a matching list or dictionary.
- shapetuple or _unspecified
The shape of the timeseries output variable. This must be provided (if not scalar) since Dymos doesn’t necessarily know the shape of ODE outputs until setup time.
- timeseriesstr or None
The name of the timeseries to which the output is being added.
- **kwargs
Additional arguments passed to the exec comp.
Interpolated Timeseries Outputs#
Sometimes a user may want to interpolate the results of a phase onto a different grid. This is particularly
useful in the context of tandem phases. Additional timeseries may be added to a phase using the add_timeseries method. By default all timeseries will provide times, states, controls, and parameters on the specified output grid. Adding other variables is accomplished using the
timeseries argument in the add_timeseries_output method.
- Phase.add_timeseries(name, transcription, subset='all')[source]
Adds a new timeseries output upon which outputs can be provided.
- Parameters:
- namestr
A name for the timeseries output path.
- transcriptionstr
A transcription object which provides a grid upon which the outputs of the timeseries are provided.
- subsetstr
The name of the node subset in the given transcription at which outputs are to be provided.
Interpolating Timeseries Outputs#
Outputs from the timeseries are provided at the node resolution used to solve the problem. Sometimes it is useful to visualize the data at a different resolution - for instance to see oscillatory behavior in the solution that may not be noticeable by only viewing the solution nodes.
The Phase.interp method allows nodes to be provided as a sequence in the “tau space” (nondimensional time) of the phase. In phase tau space, the time-like variable is -1 at the start of the phase and +1 at the end of the phase.
For instance, let’s say we want to solve the minimum time climb example and plot the control solution at 100 nodes equally spaced throughout the phase.
import numpy as np
import matplotlib.pyplot as plt
from dymos.examples.min_time_climb.min_time_climb_ode import MinTimeClimbODE
p = om.Problem(model=om.Group())
p.driver = om.pyOptSparseDriver()
p.driver.options['optimizer'] = 'IPOPT'
p.driver.options['print_results'] = 'minimal'
p.driver.declare_coloring()
p.driver.opt_settings['tol'] = 1.0E-5
p.driver.opt_settings['print_level'] = 0
p.driver.opt_settings['mu_strategy'] = 'monotone'
p.driver.opt_settings['bound_mult_init_method'] = 'mu-based'
p.driver.opt_settings['mu_init'] = 0.01
tx = dm.Radau(num_segments=8, order=3)
traj = dm.Trajectory()
phase = dm.Phase(ode_class=MinTimeClimbODE, transcription=tx)
traj.add_phase('phase0', phase)
p.model.add_subsystem('traj', traj)
phase.set_time_options(fix_initial=True, duration_bounds=(50, 400),
duration_ref=100.0)
phase.add_state('r', fix_initial=True, lower=0, upper=1.0E6,
ref=1.0E3, defect_ref=1.0E3, units='m',
rate_source='flight_dynamics.r_dot')
phase.add_state('h', fix_initial=True, lower=0, upper=20000.0,
ref=20_000, defect_ref=20_000, units='m',
rate_source='flight_dynamics.h_dot', targets=['h'])
phase.add_state('v', fix_initial=True, lower=10.0,
ref=1.0E2, defect_ref=1.0E2, units='m/s',
rate_source='flight_dynamics.v_dot', targets=['v'])
phase.add_state('gam', fix_initial=True, lower=-1.5, upper=1.5,
ref=1.0, defect_ref=1.0, units='rad',
rate_source='flight_dynamics.gam_dot', targets=['gam'])
phase.add_state('m', fix_initial=True, lower=10.0, upper=1.0E5,
ref=10_000, defect_ref=10_000, units='kg',
rate_source='prop.m_dot', targets=['m'])
phase.add_control('alpha', units='deg', lower=-8.0, upper=8.0, scaler=1.0,
rate_continuity=True, rate_continuity_scaler=100.0,
rate2_continuity=False, targets=['alpha'])
phase.add_parameter('S', val=49.2386, units='m**2', opt=False, targets=['S'])
phase.add_parameter('Isp', val=1600.0, units='s', opt=False, targets=['Isp'])
phase.add_parameter('throttle', val=1.0, opt=False, targets=['throttle'])
phase.add_boundary_constraint('h', loc='final', equals=20000, scaler=1.0E-3)
phase.add_boundary_constraint('aero.mach', loc='final', equals=1.0)
phase.add_boundary_constraint('gam', loc='final', equals=0.0)
phase.add_path_constraint(name='h', lower=100.0, upper=20000, ref=20000)
phase.add_path_constraint(name='aero.mach', lower=0.1, upper=1.8)
# Minimize time at the end of the phase
phase.add_objective('time', loc='final', ref=1.0)
# test mixing wildcard ODE variable expansion and unit overrides
phase.add_timeseries_output(['aero.*', 'prop.thrust', 'prop.m_dot'],
units={'aero.f_lift': 'lbf', 'prop.thrust': 'lbf'})
p.model.linear_solver = om.DirectSolver()
p.setup(check=True)
p['traj.phase0.t_initial'] = 0.0
p['traj.phase0.t_duration'] = 350.0
phase.set_time_val(initial=0.0, duration=350.0)
phase.set_state_val('r', [0.0, 111319.54])
phase.set_state_val('h', [100.0, 20000.0])
phase.set_state_val('v', [135.964, 283.159])
phase.set_state_val('gam', [0.0, 0.0])
phase.set_state_val('m', [19030.468, 16841.431])
phase.set_control_val('alpha', [0.0, 0.0])
dm.run_problem(p)
INFO: checking out_of_order...
INFO: out_of_order check complete (0.000868 sec).
INFO: checking system...
INFO: system check complete (0.000036 sec).
INFO: checking solvers...
INFO: solvers check complete (0.000375 sec).
INFO: checking dup_inputs...
INFO: dup_inputs check complete (0.000140 sec).
INFO: checking missing_recorders...
INFO: missing_recorders check complete (0.000003 sec).
INFO: checking unserializable_options...
INFO: unserializable_options check complete (0.001606 sec).
INFO: checking comp_has_no_outputs...
INFO: comp_has_no_outputs check complete (0.000070 sec).
INFO: checking auto_ivc_warnings...
INFO: auto_ivc_warnings check complete (0.000004 sec).
INFO: checking out_of_order...
INFO: out_of_order check complete (0.000337 sec).
INFO: checking system...
INFO: system check complete (0.000031 sec).
INFO: checking solvers...
INFO: solvers check complete (0.000293 sec).
INFO: checking dup_inputs...
INFO: dup_inputs check complete (0.000129 sec).
INFO: checking missing_recorders...
INFO: missing_recorders check complete (0.000002 sec).
INFO: checking unserializable_options...
INFO: unserializable_options check complete (0.001471 sec).
INFO: checking comp_has_no_outputs...
INFO: comp_has_no_outputs check complete (0.000059 sec).
INFO: checking auto_ivc_warnings...
INFO: auto_ivc_warnings check complete (0.000002 sec).
/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/recorders/sqlite_recorder.py:231: UserWarning:The existing case recorder file, /home/runner/work/dymos/dymos/docs/dymos_book/features/phases/problem_out/dymos_solution.db, is being overwritten.
INFO: checking out_of_order...
INFO: out_of_order check complete (0.000330 sec).
INFO: checking system...
INFO: system check complete (0.000026 sec).
INFO: checking solvers...
INFO: solvers check complete (0.000185 sec).
INFO: checking dup_inputs...
INFO: dup_inputs check complete (0.000073 sec).
INFO: checking missing_recorders...
INFO: missing_recorders check complete (0.000002 sec).
INFO: checking unserializable_options...
INFO: unserializable_options check complete (0.001262 sec).
INFO: checking comp_has_no_outputs...
INFO: comp_has_no_outputs check complete (0.000043 sec).
INFO: checking auto_ivc_warnings...
INFO: auto_ivc_warnings check complete (0.000002 sec).
Jacobian shape: (200, 145) (4.17% nonzero)
FWD solves: 17 REV solves: 0
Total colors vs. total size: 17 vs 145 (88.28% improvement)
Sparsity computed using tolerance: 1e-25.
Dense total jacobian for Problem 'problem' was computed 3 times.
Time to compute sparsity: 0.0741 sec
Time to compute coloring: 0.1807 sec
Memory to compute coloring: 0.1250 MB
Coloring created on: 2025-06-24 17:47:54
/usr/share/miniconda/envs/test/lib/python3.11/site-packages/openmdao/core/total_jac.py:1731: DerivativesWarning:Constraints or objectives [('traj.phase0.h[path]', inds=[(0, 0)]), ('traj.phase0.mach[path]', inds=[(0, 0)])] cannot be impacted by the design variables of the problem.
minimal_print is not available for this solution
Optimization Problem -- Optimization using pyOpt_sparse
================================================================================
Objective Function: _objfunc
Solution:
--------------------------------------------------------------------------------
Total Time: 6.0016
User Objective Time : 2.7745
User Sensitivity Time : 1.6999
Interface Time : 0.7234
Opt Solver Time: 0.8038
Calls to Objective Function : 393
Calls to Sens Function : 170
Objectives
Index Name Value
0 traj.phase0.t 3.253204E+02
Variables (c - continuous, i - integer, d - discrete)
Index Name Type Lower Bound Value Upper Bound Status
0 traj.phase0.t_duration_0 c 5.000000E-01 3.253204E+00 4.000000E+00
1 traj.phase0.states:r_0 c 0.000000E+00 2.637841E+00 1.000000E+03
2 traj.phase0.states:r_1 c 0.000000E+00 7.739039E+00 1.000000E+03
3 traj.phase0.states:r_2 c 0.000000E+00 9.490996E+00 1.000000E+03
4 traj.phase0.states:r_3 c 0.000000E+00 1.327358E+01 1.000000E+03
5 traj.phase0.states:r_4 c 0.000000E+00 1.833264E+01 1.000000E+03
6 traj.phase0.states:r_5 c 0.000000E+00 1.996973E+01 1.000000E+03
7 traj.phase0.states:r_6 c 0.000000E+00 2.400240E+01 1.000000E+03
8 traj.phase0.states:r_7 c 0.000000E+00 3.025521E+01 1.000000E+03
9 traj.phase0.states:r_8 c 0.000000E+00 3.242127E+01 1.000000E+03
10 traj.phase0.states:r_9 c 0.000000E+00 3.780651E+01 1.000000E+03
11 traj.phase0.states:r_10 c 0.000000E+00 4.608205E+01 1.000000E+03
12 traj.phase0.states:r_11 c 0.000000E+00 4.885167E+01 1.000000E+03
13 traj.phase0.states:r_12 c 0.000000E+00 5.518483E+01 1.000000E+03
14 traj.phase0.states:r_13 c 0.000000E+00 6.405459E+01 1.000000E+03
15 traj.phase0.states:r_14 c 0.000000E+00 6.691002E+01 1.000000E+03
16 traj.phase0.states:r_15 c 0.000000E+00 7.362473E+01 1.000000E+03
17 traj.phase0.states:r_16 c 0.000000E+00 8.329902E+01 1.000000E+03
18 traj.phase0.states:r_17 c 0.000000E+00 8.646722E+01 1.000000E+03
19 traj.phase0.states:r_18 c 0.000000E+00 9.388696E+01 1.000000E+03
20 traj.phase0.states:r_19 c 0.000000E+00 1.038338E+02 1.000000E+03
21 traj.phase0.states:r_20 c 0.000000E+00 1.067134E+02 1.000000E+03
22 traj.phase0.states:r_21 c 0.000000E+00 1.119502E+02 1.000000E+03
23 traj.phase0.states:r_22 c 0.000000E+00 1.177690E+02 1.000000E+03
24 traj.phase0.states:r_23 c 0.000000E+00 1.196756E+02 1.000000E+03
25 traj.phase0.states:h_0 c 0.000000E+00 4.999997E-03 1.000000E+00
26 traj.phase0.states:h_1 c 0.000000E+00 6.309066E-02 1.000000E+00
27 traj.phase0.states:h_2 c 0.000000E+00 1.121187E-01 1.000000E+00
28 traj.phase0.states:h_3 c 0.000000E+00 2.248128E-01 1.000000E+00
29 traj.phase0.states:h_4 c 0.000000E+00 3.707362E-01 1.000000E+00
30 traj.phase0.states:h_5 c 0.000000E+00 4.035150E-01 1.000000E+00
31 traj.phase0.states:h_6 c 0.000000E+00 4.460695E-01 1.000000E+00
32 traj.phase0.states:h_7 c 0.000000E+00 4.381599E-01 1.000000E+00
33 traj.phase0.states:h_8 c 0.000000E+00 4.216803E-01 1.000000E+00
34 traj.phase0.states:h_9 c 0.000000E+00 3.787950E-01 1.000000E+00
35 traj.phase0.states:h_10 c 0.000000E+00 3.493045E-01 1.000000E+00
36 traj.phase0.states:h_11 c 0.000000E+00 3.567526E-01 1.000000E+00
37 traj.phase0.states:h_12 c 0.000000E+00 3.853665E-01 1.000000E+00
38 traj.phase0.states:h_13 c 0.000000E+00 4.275798E-01 1.000000E+00
39 traj.phase0.states:h_14 c 0.000000E+00 4.347830E-01 1.000000E+00
40 traj.phase0.states:h_15 c 0.000000E+00 4.442898E-01 1.000000E+00
41 traj.phase0.states:h_16 c 0.000000E+00 4.487381E-01 1.000000E+00
42 traj.phase0.states:h_17 c 0.000000E+00 4.508781E-01 1.000000E+00
43 traj.phase0.states:h_18 c 0.000000E+00 4.651480E-01 1.000000E+00
44 traj.phase0.states:h_19 c 0.000000E+00 5.588391E-01 1.000000E+00
45 traj.phase0.states:h_20 c 0.000000E+00 6.204696E-01 1.000000E+00
46 traj.phase0.states:h_21 c 0.000000E+00 7.973560E-01 1.000000E+00
47 traj.phase0.states:h_22 c 0.000000E+00 9.850850E-01 1.000000E+00
48 traj.phase0.states:h_23 c 0.000000E+00 1.000000E+00 1.000000E+00 u
49 traj.phase0.states:v_0 c 1.000000E-01 2.229877E+00 1.000000E+19
50 traj.phase0.states:v_1 c 1.000000E-01 3.039676E+00 1.000000E+19
51 traj.phase0.states:v_2 c 1.000000E-01 3.066592E+00 1.000000E+19
52 traj.phase0.states:v_3 c 1.000000E-01 3.022227E+00 1.000000E+19
53 traj.phase0.states:v_4 c 1.000000E-01 2.828284E+00 1.000000E+19
54 traj.phase0.states:v_5 c 1.000000E-01 2.811672E+00 1.000000E+19
55 traj.phase0.states:v_6 c 1.000000E-01 2.943774E+00 1.000000E+19
56 traj.phase0.states:v_7 c 1.000000E-01 3.386841E+00 1.000000E+19
57 traj.phase0.states:v_8 c 1.000000E-01 3.559157E+00 1.000000E+19
58 traj.phase0.states:v_9 c 1.000000E-01 3.969504E+00 1.000000E+19
59 traj.phase0.states:v_10 c 1.000000E-01 4.345898E+00 1.000000E+19
60 traj.phase0.states:v_11 c 1.000000E-01 4.380089E+00 1.000000E+19
61 traj.phase0.states:v_12 c 1.000000E-01 4.431640E+00 1.000000E+19
62 traj.phase0.states:v_13 c 1.000000E-01 4.517314E+00 1.000000E+19
63 traj.phase0.states:v_14 c 1.000000E-01 4.574615E+00 1.000000E+19
64 traj.phase0.states:v_15 c 1.000000E-01 4.734367E+00 1.000000E+19
65 traj.phase0.states:v_16 c 1.000000E-01 4.983114E+00 1.000000E+19
66 traj.phase0.states:v_17 c 1.000000E-01 5.055009E+00 1.000000E+19
67 traj.phase0.states:v_18 c 1.000000E-01 5.177031E+00 1.000000E+19
68 traj.phase0.states:v_19 c 1.000000E-01 4.990167E+00 1.000000E+19
69 traj.phase0.states:v_20 c 1.000000E-01 4.776167E+00 1.000000E+19
70 traj.phase0.states:v_21 c 1.000000E-01 4.012747E+00 1.000000E+19
71 traj.phase0.states:v_22 c 1.000000E-01 3.067220E+00 1.000000E+19
72 traj.phase0.states:v_23 c 1.000000E-01 2.950719E+00 1.000000E+19
73 traj.phase0.states:gam_0 c -1.500000E+00 4.619589E-02 1.500000E+00
74 traj.phase0.states:gam_1 c -1.500000E+00 4.272143E-01 1.500000E+00
75 traj.phase0.states:gam_2 c -1.500000E+00 4.879831E-01 1.500000E+00
76 traj.phase0.states:gam_3 c -1.500000E+00 5.639945E-01 1.500000E+00
77 traj.phase0.states:gam_4 c -1.500000E+00 4.317060E-01 1.500000E+00
78 traj.phase0.states:gam_5 c -1.500000E+00 3.265088E-01 1.500000E+00
79 traj.phase0.states:gam_6 c -1.500000E+00 9.876691E-02 1.500000E+00
80 traj.phase0.states:gam_7 c -1.500000E+00 -1.255408E-01 1.500000E+00
81 traj.phase0.states:gam_8 c -1.500000E+00 -1.629673E-01 1.500000E+00
82 traj.phase0.states:gam_9 c -1.500000E+00 -1.392728E-01 1.500000E+00
83 traj.phase0.states:gam_10 c -1.500000E+00 1.665479E-02 1.500000E+00
84 traj.phase0.states:gam_11 c -1.500000E+00 6.494207E-02 1.500000E+00
85 traj.phase0.states:gam_12 c -1.500000E+00 1.053951E-01 1.500000E+00
86 traj.phase0.states:gam_13 c -1.500000E+00 6.666110E-02 1.500000E+00
87 traj.phase0.states:gam_14 c -1.500000E+00 4.591413E-02 1.500000E+00
88 traj.phase0.states:gam_15 c -1.500000E+00 1.498449E-02 1.500000E+00
89 traj.phase0.states:gam_16 c -1.500000E+00 1.038283E-02 1.500000E+00
90 traj.phase0.states:gam_17 c -1.500000E+00 1.850410E-02 1.500000E+00
91 traj.phase0.states:gam_18 c -1.500000E+00 7.525432E-02 1.500000E+00
92 traj.phase0.states:gam_19 c -1.500000E+00 3.387753E-01 1.500000E+00
93 traj.phase0.states:gam_20 c -1.500000E+00 4.862925E-01 1.500000E+00
94 traj.phase0.states:gam_21 c -1.500000E+00 6.652379E-01 1.500000E+00
95 traj.phase0.states:gam_22 c -1.500000E+00 3.073222E-01 1.500000E+00
96 traj.phase0.states:gam_23 c -1.500000E+00 0.000000E+00 1.500000E+00
97 traj.phase0.states:m_0 c 1.000000E-03 1.890596E+00 1.000000E+01
98 traj.phase0.states:m_1 c 1.000000E-03 1.871835E+00 1.000000E+01
99 traj.phase0.states:m_2 c 1.000000E-03 1.865977E+00 1.000000E+01
100 traj.phase0.states:m_3 c 1.000000E-03 1.854296E+00 1.000000E+01
101 traj.phase0.states:m_4 c 1.000000E-03 1.841664E+00 1.000000E+01
102 traj.phase0.states:m_5 c 1.000000E-03 1.838504E+00 1.000000E+01
103 traj.phase0.states:m_6 c 1.000000E-03 1.831626E+00 1.000000E+01
104 traj.phase0.states:m_7 c 1.000000E-03 1.821751E+00 1.000000E+01
105 traj.phase0.states:m_8 c 1.000000E-03 1.818164E+00 1.000000E+01
106 traj.phase0.states:m_9 c 1.000000E-03 1.808560E+00 1.000000E+01
107 traj.phase0.states:m_10 c 1.000000E-03 1.792731E+00 1.000000E+01
108 traj.phase0.states:m_11 c 1.000000E-03 1.787323E+00 1.000000E+01
109 traj.phase0.states:m_12 c 1.000000E-03 1.775341E+00 1.000000E+01
110 traj.phase0.states:m_13 c 1.000000E-03 1.759503E+00 1.000000E+01
111 traj.phase0.states:m_14 c 1.000000E-03 1.754666E+00 1.000000E+01
112 traj.phase0.states:m_15 c 1.000000E-03 1.743366E+00 1.000000E+01
113 traj.phase0.states:m_16 c 1.000000E-03 1.727256E+00 1.000000E+01
114 traj.phase0.states:m_17 c 1.000000E-03 1.721989E+00 1.000000E+01
115 traj.phase0.states:m_18 c 1.000000E-03 1.709806E+00 1.000000E+01
116 traj.phase0.states:m_19 c 1.000000E-03 1.694530E+00 1.000000E+01
117 traj.phase0.states:m_20 c 1.000000E-03 1.690605E+00 1.000000E+01
118 traj.phase0.states:m_21 c 1.000000E-03 1.685074E+00 1.000000E+01
119 traj.phase0.states:m_22 c 1.000000E-03 1.682152E+00 1.000000E+01
120 traj.phase0.states:m_23 c 1.000000E-03 1.681652E+00 1.000000E+01
121 traj.phase0.controls:alpha_0 c -8.000000E+00 4.289003E+00 8.000000E+00
122 traj.phase0.controls:alpha_1 c -8.000000E+00 2.743099E+00 8.000000E+00
123 traj.phase0.controls:alpha_2 c -8.000000E+00 1.583494E+00 8.000000E+00
124 traj.phase0.controls:alpha_3 c -8.000000E+00 1.451646E+00 8.000000E+00
125 traj.phase0.controls:alpha_4 c -8.000000E+00 1.318110E+00 8.000000E+00
126 traj.phase0.controls:alpha_5 c -8.000000E+00 1.261671E+00 8.000000E+00
127 traj.phase0.controls:alpha_6 c -8.000000E+00 1.274686E+00 8.000000E+00
128 traj.phase0.controls:alpha_7 c -8.000000E+00 1.348983E+00 8.000000E+00
129 traj.phase0.controls:alpha_8 c -8.000000E+00 1.541786E+00 8.000000E+00
130 traj.phase0.controls:alpha_9 c -8.000000E+00 1.624619E+00 8.000000E+00
131 traj.phase0.controls:alpha_10 c -8.000000E+00 1.735722E+00 8.000000E+00
132 traj.phase0.controls:alpha_11 c -8.000000E+00 1.591575E+00 8.000000E+00
133 traj.phase0.controls:alpha_12 c -8.000000E+00 1.474095E+00 8.000000E+00
134 traj.phase0.controls:alpha_13 c -8.000000E+00 1.233285E+00 8.000000E+00
135 traj.phase0.controls:alpha_14 c -8.000000E+00 1.123528E+00 8.000000E+00
136 traj.phase0.controls:alpha_15 c -8.000000E+00 1.142545E+00 8.000000E+00
137 traj.phase0.controls:alpha_16 c -8.000000E+00 1.209550E+00 8.000000E+00
138 traj.phase0.controls:alpha_17 c -8.000000E+00 1.281856E+00 8.000000E+00
139 traj.phase0.controls:alpha_18 c -8.000000E+00 1.299874E+00 8.000000E+00
140 traj.phase0.controls:alpha_19 c -8.000000E+00 1.664438E+00 8.000000E+00
141 traj.phase0.controls:alpha_20 c -8.000000E+00 3.237875E+00 8.000000E+00
142 traj.phase0.controls:alpha_21 c -8.000000E+00 3.994455E+00 8.000000E+00
143 traj.phase0.controls:alpha_22 c -8.000000E+00 3.797223E+00 8.000000E+00
144 traj.phase0.controls:alpha_23 c -8.000000E+00 -3.278866E+00 8.000000E+00
Constraints (i - inequality, e - equality)
Index Name Type Lower Value Upper Status Lagrange Multiplier (N/A)
0 traj.phase0.h[final] e 2.000000E+01 2.000000E+01 2.000000E+01 9.00000E+100
1 traj.phase0.mach[final] e 1.000000E+00 1.000000E+00 1.000000E+00 9.00000E+100
2 traj.phase0.gam[final] e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
3 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 -5.778852E-16 0.000000E+00 9.00000E+100
4 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.311541E-15 0.000000E+00 9.00000E+100
5 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.391928E-14 0.000000E+00 9.00000E+100
6 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 6.356737E-14 0.000000E+00 9.00000E+100
7 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 9.246163E-15 0.000000E+00 9.00000E+100
8 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 -5.778852E-15 0.000000E+00 9.00000E+100
9 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 -2.542695E-14 0.000000E+00 9.00000E+100
10 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.467311E-15 0.000000E+00 9.00000E+100
11 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.778852E-15 0.000000E+00 9.00000E+100
12 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 -1.155770E-14 0.000000E+00 9.00000E+100
13 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.733656E-14 0.000000E+00 9.00000E+100
14 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.675350E-13 0.000000E+00 9.00000E+100
15 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.559256E-13 0.000000E+00 9.00000E+100
16 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 3.894946E-13 0.000000E+00 9.00000E+100
17 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 2.542695E-14 0.000000E+00 9.00000E+100
18 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 -3.236157E-14 0.000000E+00 9.00000E+100
19 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 1.178886E-13 0.000000E+00 9.00000E+100
20 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.241677E-13 0.000000E+00 9.00000E+100
21 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.027601E-13 0.000000E+00 9.00000E+100
22 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.068312E-13 0.000000E+00 9.00000E+100
23 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 -2.773849E-14 0.000000E+00 9.00000E+100
24 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 5.085390E-14 0.000000E+00 9.00000E+100
25 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 4.079870E-13 0.000000E+00 9.00000E+100
26 traj.phase0.collocation_constraint.defects:r e 0.000000E+00 6.819045E-14 0.000000E+00 9.00000E+100
27 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -2.273737E-17 0.000000E+00 9.00000E+100
28 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.083535E-17 0.000000E+00 9.00000E+100
29 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 3.149474E-15 0.000000E+00 9.00000E+100
30 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 6.414526E-15 0.000000E+00 9.00000E+100
31 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 6.530103E-15 0.000000E+00 9.00000E+100
32 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.456012E-15 0.000000E+00 9.00000E+100
33 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.643825E-15 0.000000E+00 9.00000E+100
34 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.134100E-15 0.000000E+00 9.00000E+100
35 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.791444E-15 0.000000E+00 9.00000E+100
36 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.889426E-15 0.000000E+00 9.00000E+100
37 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.950363E-15 0.000000E+00 9.00000E+100
38 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -2.123728E-15 0.000000E+00 9.00000E+100
39 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 6.725139E-15 0.000000E+00 9.00000E+100
40 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 2.059438E-14 0.000000E+00 9.00000E+100
41 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 8.830808E-15 0.000000E+00 9.00000E+100
42 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.379701E-15 0.000000E+00 9.00000E+100
43 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.158931E-14 0.000000E+00 9.00000E+100
44 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -7.927863E-15 0.000000E+00 9.00000E+100
45 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -2.412671E-15 0.000000E+00 9.00000E+100
46 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 1.113874E-14 0.000000E+00 9.00000E+100
47 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 5.374332E-15 0.000000E+00 9.00000E+100
48 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -2.918320E-15 0.000000E+00 9.00000E+100
49 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.531396E-15 0.000000E+00 9.00000E+100
50 traj.phase0.collocation_constraint.defects:h e 0.000000E+00 -1.069088E-15 0.000000E+00 9.00000E+100
51 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 9.029456E-16 0.000000E+00 9.00000E+100
52 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.083535E-15 0.000000E+00 9.00000E+100
53 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 3.295752E-14 0.000000E+00 9.00000E+100
54 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.373606E-13 0.000000E+00 9.00000E+100
55 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 3.021933E-13 0.000000E+00 9.00000E+100
56 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.301383E-13 0.000000E+00 9.00000E+100
57 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.915555E-13 0.000000E+00 9.00000E+100
58 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.549918E-13 0.000000E+00 9.00000E+100
59 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 -2.889426E-15 0.000000E+00 9.00000E+100
60 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.137711E-14 0.000000E+00 9.00000E+100
61 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 6.121971E-14 0.000000E+00 9.00000E+100
62 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 9.977549E-15 0.000000E+00 9.00000E+100
63 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 -3.544062E-15 0.000000E+00 9.00000E+100
64 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.201821E-13 0.000000E+00 9.00000E+100
65 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 3.155795E-13 0.000000E+00 9.00000E+100
66 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 3.384466E-13 0.000000E+00 9.00000E+100
67 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 2.787845E-13 0.000000E+00 9.00000E+100
68 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 5.954926E-14 0.000000E+00 9.00000E+100
69 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.101594E-14 0.000000E+00 9.00000E+100
70 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 4.858976E-14 0.000000E+00 9.00000E+100
71 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 3.454670E-13 0.000000E+00 9.00000E+100
72 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 6.121971E-14 0.000000E+00 9.00000E+100
73 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 -5.652440E-14 0.000000E+00 9.00000E+100
74 traj.phase0.collocation_constraint.defects:v e 0.000000E+00 1.216268E-13 0.000000E+00 9.00000E+100
75 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -1.763566E-16 0.000000E+00 9.00000E+100
76 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 7.054263E-16 0.000000E+00 9.00000E+100
77 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -2.116279E-15 0.000000E+00 9.00000E+100
78 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -3.812829E-14 0.000000E+00 9.00000E+100
79 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -7.609565E-14 0.000000E+00 9.00000E+100
80 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -3.054496E-14 0.000000E+00 9.00000E+100
81 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -2.715891E-14 0.000000E+00 9.00000E+100
82 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 2.708131E-13 0.000000E+00 9.00000E+100
83 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 1.499031E-15 0.000000E+00 9.00000E+100
84 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 3.757277E-14 0.000000E+00 9.00000E+100
85 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -1.899360E-14 0.000000E+00 9.00000E+100
86 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -3.262597E-14 0.000000E+00 9.00000E+100
87 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -2.130387E-14 0.000000E+00 9.00000E+100
88 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -1.519753E-14 0.000000E+00 9.00000E+100
89 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -1.939922E-16 0.000000E+00 9.00000E+100
90 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 8.350484E-15 0.000000E+00 9.00000E+100
91 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 1.406003E-14 0.000000E+00 9.00000E+100
92 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -1.214876E-14 0.000000E+00 9.00000E+100
93 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -1.771061E-14 0.000000E+00 9.00000E+100
94 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -1.257422E-14 0.000000E+00 9.00000E+100
95 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -6.327674E-14 0.000000E+00 9.00000E+100
96 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -6.468759E-14 0.000000E+00 9.00000E+100
97 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 3.857800E-14 0.000000E+00 9.00000E+100
98 traj.phase0.collocation_constraint.defects:gam e 0.000000E+00 -3.484806E-14 0.000000E+00 9.00000E+100
99 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 1.126876E-15 0.000000E+00 9.00000E+100
100 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -5.164849E-16 0.000000E+00 9.00000E+100
101 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -7.512508E-16 0.000000E+00 9.00000E+100
102 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -1.986480E-16 0.000000E+00 9.00000E+100
103 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
104 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 9.751813E-17 0.000000E+00 9.00000E+100
105 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 1.807697E-15 0.000000E+00 9.00000E+100
106 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 2.744955E-16 0.000000E+00 9.00000E+100
107 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -1.132294E-15 0.000000E+00 9.00000E+100
108 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 5.020378E-16 0.000000E+00 9.00000E+100
109 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 8.957221E-16 0.000000E+00 9.00000E+100
110 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 3.106133E-16 0.000000E+00 9.00000E+100
111 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 8.668278E-17 0.000000E+00 9.00000E+100
112 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -1.986480E-16 0.000000E+00 9.00000E+100
113 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 9.535106E-16 0.000000E+00 9.00000E+100
114 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -3.358958E-16 0.000000E+00 9.00000E+100
115 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -9.029456E-17 0.000000E+00 9.00000E+100
116 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -1.094370E-15 0.000000E+00 9.00000E+100
117 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 9.318399E-16 0.000000E+00 9.00000E+100
118 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -2.817190E-16 0.000000E+00 9.00000E+100
119 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 -1.930498E-15 0.000000E+00 9.00000E+100
120 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 2.687166E-15 0.000000E+00 9.00000E+100
121 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 2.690778E-16 0.000000E+00 9.00000E+100
122 traj.phase0.collocation_constraint.defects:m e 0.000000E+00 1.358933E-16 0.000000E+00 9.00000E+100
123 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 1.072248E-12 0.000000E+00 9.00000E+100
124 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
125 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 1.072248E-12 0.000000E+00 9.00000E+100
126 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
127 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
128 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 3.527131E-13 0.000000E+00 9.00000E+100
129 traj.phase0.continuity_comp.defect_control_rates:alpha_rate e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
130 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 2.220446E-16 0.000000E+00 9.00000E+100
131 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 -2.220446E-16 0.000000E+00 9.00000E+100
132 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 0.000000E+00 0.000000E+00 9.00000E+100
133 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 -2.220446E-16 0.000000E+00 9.00000E+100
134 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 2.220446E-16 0.000000E+00 9.00000E+100
135 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 2.220446E-16 0.000000E+00 9.00000E+100
136 traj.phase0.continuity_comp.defect_controls:alpha e 0.000000E+00 1.332268E-15 0.000000E+00 9.00000E+100
137 traj.phase0.h[path] i 5.000000E-03 5.000000E-03 1.000000E+00 l 9.00000E+100
138 traj.phase0.h[path] i 5.000000E-03 4.999997E-03 1.000000E+00 l 9.00000E+100
139 traj.phase0.h[path] i 5.000000E-03 6.309066E-02 1.000000E+00 9.00000E+100
140 traj.phase0.h[path] i 5.000000E-03 1.121187E-01 1.000000E+00 9.00000E+100
141 traj.phase0.h[path] i 5.000000E-03 1.121187E-01 1.000000E+00 9.00000E+100
142 traj.phase0.h[path] i 5.000000E-03 2.248128E-01 1.000000E+00 9.00000E+100
143 traj.phase0.h[path] i 5.000000E-03 3.707362E-01 1.000000E+00 9.00000E+100
144 traj.phase0.h[path] i 5.000000E-03 4.035150E-01 1.000000E+00 9.00000E+100
145 traj.phase0.h[path] i 5.000000E-03 4.035150E-01 1.000000E+00 9.00000E+100
146 traj.phase0.h[path] i 5.000000E-03 4.460695E-01 1.000000E+00 9.00000E+100
147 traj.phase0.h[path] i 5.000000E-03 4.381599E-01 1.000000E+00 9.00000E+100
148 traj.phase0.h[path] i 5.000000E-03 4.216803E-01 1.000000E+00 9.00000E+100
149 traj.phase0.h[path] i 5.000000E-03 4.216803E-01 1.000000E+00 9.00000E+100
150 traj.phase0.h[path] i 5.000000E-03 3.787950E-01 1.000000E+00 9.00000E+100
151 traj.phase0.h[path] i 5.000000E-03 3.493045E-01 1.000000E+00 9.00000E+100
152 traj.phase0.h[path] i 5.000000E-03 3.567526E-01 1.000000E+00 9.00000E+100
153 traj.phase0.h[path] i 5.000000E-03 3.567526E-01 1.000000E+00 9.00000E+100
154 traj.phase0.h[path] i 5.000000E-03 3.853665E-01 1.000000E+00 9.00000E+100
155 traj.phase0.h[path] i 5.000000E-03 4.275798E-01 1.000000E+00 9.00000E+100
156 traj.phase0.h[path] i 5.000000E-03 4.347830E-01 1.000000E+00 9.00000E+100
157 traj.phase0.h[path] i 5.000000E-03 4.347830E-01 1.000000E+00 9.00000E+100
158 traj.phase0.h[path] i 5.000000E-03 4.442898E-01 1.000000E+00 9.00000E+100
159 traj.phase0.h[path] i 5.000000E-03 4.487381E-01 1.000000E+00 9.00000E+100
160 traj.phase0.h[path] i 5.000000E-03 4.508781E-01 1.000000E+00 9.00000E+100
161 traj.phase0.h[path] i 5.000000E-03 4.508781E-01 1.000000E+00 9.00000E+100
162 traj.phase0.h[path] i 5.000000E-03 4.651480E-01 1.000000E+00 9.00000E+100
163 traj.phase0.h[path] i 5.000000E-03 5.588391E-01 1.000000E+00 9.00000E+100
164 traj.phase0.h[path] i 5.000000E-03 6.204696E-01 1.000000E+00 9.00000E+100
165 traj.phase0.h[path] i 5.000000E-03 6.204696E-01 1.000000E+00 9.00000E+100
166 traj.phase0.h[path] i 5.000000E-03 7.973560E-01 1.000000E+00 9.00000E+100
167 traj.phase0.h[path] i 5.000000E-03 9.850850E-01 1.000000E+00 9.00000E+100
168 traj.phase0.mach[path] i 1.000000E-01 4.000084E-01 1.800000E+00 9.00000E+100
169 traj.phase0.mach[path] i 1.000000E-01 6.560335E-01 1.800000E+00 9.00000E+100
170 traj.phase0.mach[path] i 1.000000E-01 9.062571E-01 1.800000E+00 9.00000E+100
171 traj.phase0.mach[path] i 1.000000E-01 9.248646E-01 1.800000E+00 9.00000E+100
172 traj.phase0.mach[path] i 1.000000E-01 9.248646E-01 1.800000E+00 9.00000E+100
173 traj.phase0.mach[path] i 1.000000E-01 9.368870E-01 1.800000E+00 9.00000E+100
174 traj.phase0.mach[path] i 1.000000E-01 9.106934E-01 1.800000E+00 9.00000E+100
175 traj.phase0.mach[path] i 1.000000E-01 9.134695E-01 1.800000E+00 9.00000E+100
176 traj.phase0.mach[path] i 1.000000E-01 9.134695E-01 1.800000E+00 9.00000E+100
177 traj.phase0.mach[path] i 1.000000E-01 9.677791E-01 1.800000E+00 9.00000E+100
178 traj.phase0.mach[path] i 1.000000E-01 1.110968E+00 1.800000E+00 9.00000E+100
179 traj.phase0.mach[path] i 1.000000E-01 1.162135E+00 1.800000E+00 9.00000E+100
180 traj.phase0.mach[path] i 1.000000E-01 1.162135E+00 1.800000E+00 9.00000E+100
181 traj.phase0.mach[path] i 1.000000E-01 1.280952E+00 1.800000E+00 9.00000E+100
182 traj.phase0.mach[path] i 1.000000E-01 1.391324E+00 1.800000E+00 9.00000E+100
183 traj.phase0.mach[path] i 1.000000E-01 1.405068E+00 1.800000E+00 9.00000E+100
184 traj.phase0.mach[path] i 1.000000E-01 1.405068E+00 1.800000E+00 9.00000E+100
185 traj.phase0.mach[path] i 1.000000E-01 1.432640E+00 1.800000E+00 9.00000E+100
186 traj.phase0.mach[path] i 1.000000E-01 1.477416E+00 1.800000E+00 9.00000E+100
187 traj.phase0.mach[path] i 1.000000E-01 1.499169E+00 1.800000E+00 9.00000E+100
188 traj.phase0.mach[path] i 1.000000E-01 1.499169E+00 1.800000E+00 9.00000E+100
189 traj.phase0.mach[path] i 1.000000E-01 1.555666E+00 1.800000E+00 9.00000E+100
190 traj.phase0.mach[path] i 1.000000E-01 1.639453E+00 1.800000E+00 9.00000E+100
191 traj.phase0.mach[path] i 1.000000E-01 1.664111E+00 1.800000E+00 9.00000E+100
192 traj.phase0.mach[path] i 1.000000E-01 1.664111E+00 1.800000E+00 9.00000E+100
193 traj.phase0.mach[path] i 1.000000E-01 1.711187E+00 1.800000E+00 9.00000E+100
194 traj.phase0.mach[path] i 1.000000E-01 1.691710E+00 1.800000E+00 9.00000E+100
195 traj.phase0.mach[path] i 1.000000E-01 1.618692E+00 1.800000E+00 9.00000E+100
196 traj.phase0.mach[path] i 1.000000E-01 1.618692E+00 1.800000E+00 9.00000E+100
197 traj.phase0.mach[path] i 1.000000E-01 1.359961E+00 1.800000E+00 9.00000E+100
198 traj.phase0.mach[path] i 1.000000E-01 1.039513E+00 1.800000E+00 9.00000E+100
Exit Status
Inform Description
0 Solve Succeeded
--------------------------------------------------------------------------------
Problem: problem
Driver: pyOptSparseDriver
success : True
iterations : 394
runtime : 6.3915E+00 s
model_evals : 394
model_time : 2.6180E+00 s
deriv_evals : 170
deriv_time : 1.2053E+00 s
exit_status : SUCCESS
Now we pull the values of time and alpha from the timeseries. Remember that the timeseries provides values at the nodes only. The fitting polynomials may exhibit oscillations between these nodes.
We use cubic interpolation to interpolate time and alpha onto 100 evenly distributed nodes across the phase, and then plot the results.
t = p.get_val('traj.phase0.timeseries.time')
alpha = p.get_val('traj.phase0.timeseries.alpha', units='deg')
t_100 = phase.interp(xs=t, ys=t,
nodes=np.linspace(-1, 1, 100),
kind='cubic')
alpha_100 = phase.interp(xs=t, ys=alpha,
nodes=np.linspace(-1, 1, 100),
kind='cubic')
# Plot the solution nodes
%matplotlib inline
plt.plot(t, alpha, 'o')
plt.plot(t_100, alpha_100, '-')
plt.xlabel('time (s)')
plt.ylabel('angle of attack (deg)')
plt.grid()
plt.show()
Both the simulate method and the interp method can provide more dense output. The difference is that simulate is effectively finding a different solution for the states, by starting from the initial values and propagating the ODE forward in time using the interpolated control splines as inputs. The interp method is making some assumptions about the interpolation (for instance, cubic interpolation in this case), so it may not be a perfectly accurate representation of the underlying interpolating polynomials.