scenarioVariableTimeStepIntegrators

Overview

This script illustrates how to setup different variable time step integration methods for a basic 3-DOF orbit scenario. Both a fourth-order (RKF45) and a seventh-order (RKF78) integrators are used. For comparison, an RK4 integrator is also used.

The script is found in the folder basilisk/examples and executed by using:

python3 scenarioVariableTimeStepIntegrators.py

For more information on how to setup different integrators, see scenarioIntegrators. When the simulation completes, a plot is shown for illustrating both the true and the numerically evaluated orbit.

Illustration of Simulation Results

show_plots = True, integratorCase = {'rk4', 'rkf45', 'rkf78'}

The following figure illustrates the resulting trajectories relative to the true trajectory using a very coarse integration time step of 2 hours. The variable time step integrators still approximates the true orbit well, while the RK4 method is starting to show some visible errors, illustrating that much smaller time steps must be used with this method in this scenario.

Creating New Integrator Modules

New integration modules can be readily created for Basilisk. They are all stored in the folder Basilisk/src/simulation/dynamics/Integrators/.

The integrators must be created to function on a general state vector and be independent of the particular dynamics being integrated. Note that the default integrator is placed inside the _GeneralModulesFiles folder within the dynamics folder.

scenarioVariableTimeStepIntegrators.run(show_plots, integratorCase, relTol, absTol)

The scenarios can be run with the followings setups parameters:

Parameters:

• show_plots (bool) – Determines if the script should display plots

• integratorCase (bool) –

  Specify what type of integrator to use in the sim

  String	Definition
  ’rk4’	RK4
  ’rkf45’	RKF45
  ’rkf78’	RKF78

• relTol (double) – Specify the relative tolerance to use in the integration

• absTol (double) – Specify the absolute tolerance to use in the integration