3.1. Integrator Settings

As the name suggests, the integrator settings tell the dynamics simulator how to integrate numerically the equations of motion that govern the orbital mechanics to simulate. The IntegratorSettings are defined using four derived classes, depending on whether the integrator to be used is a fixed step-size integrator or a variable step-size integrator.

class IntegratorSettings

This class is used to define the settings for fixed step-size integration. The constructor for this base class is:

IntegratorSettings< TimeType >( integratorType,
                                simulationStartEpoch,
                                fixedStepSize )

where:

  • TimeType

    Template argument used to set the precision of the time, in general double is used. For some application where a high precision is required this can be changed to e.g. long double.

  • integratorType

    AvailableIntegrators which defines the fixed step-size integrator type to be used. Currently the only options available are euler and rungeKutta4.

  • simulationStartEpoch

    TimeType that defines the simulation’s start epoch.

  • fixedStepSize

    TimeType that defines the fixed step-size to be used either by the euler or the rungeKutta4 numerical integrator.

class RungeKuttaVariableStepSizeSettings

This class is used to define the settings for the Runge-Kutta variable step-size integration methods, where the error tolerances are defined as a scalar (i.e., each state element has the same tolerance). The constructor for this derived class is:

RungeKuttaVariableStepSizeSettings< TimeType >(
      simulationStartEpoch,
      initialTimeStep,
      coefficientSet,
      minimumStepSize,
      maximumStepSize,
      relativeErrorTolerance,
      absoluteErrorTolerance,
      saveFrequency,
      assessPropagationTerminationConditionDuringIntegrationSubsteps,
      safetyFactorForNextStepSize,
      maximumFactorIncreaseForNextStepSize,
      minimumFactorDecreaseForNextStepSize )

where:

  • TimeType

    Template argument used to set the precision of the time, in general double is used. For some application where a high precision is required this can be changed to e.g. long double.

  • simulationStartEpoch

    TimeType that defines the simulation’s initial time. It must be a double variable-type.

  • initialTimeStep

    TimeType that defines the initial step-size to be used either by the rungeKuttaVariableStepSize numerical integrator. It must be a double variable-type.

  • coefficientSet

    RungeKuttaCoefficients::CoefficientSets that defines the coefficient set to be used by the rungeKuttaVariableStepSize numerical integrator. The list of available coefficient sets is given in Integrators.

  • minimumStepSize

    TimeType that defines the minimum step-size that the rungeKuttaVariableStepSize numerical integrator can take.

  • maximumStepSize

    TimeType that defines the maximum step-size that the rungeKuttaVariableStepSize numerical integrator can take.

  • relativeErrorTolerance

    TimeType that defines the relative error tolerance for step size control of the rungeKuttaVariableStepSize numerical integrator.

  • absoluteErrorTolerance

    TimeType that defines the absolute error tolerance for step size control of the rungeKuttaVariableStepSize numerical integrator.

  • saveFrequency

    Frequency at which to save the numerical integrated states. For instance, you may want to save one every 15 time steps, to give an output that is less demanding in terms of storage (in this case 15 would be the saveFrequency). The default value is 1.

  • assessPropagationTerminationConditionDuringIntegrationSubsteps

    Whether the propagation termination conditions should be evaluated during the intermediate sub-steps of the integrator (true) or only at the end of each integration step (false). The default value is false.

  • safetyFactorForNextStepSize

    Safety factor for step size control. The default value is 0.8.

  • maximumFactorIncreaseForNextStepSize

    Maximum increase factor in time step in subsequent iterations. The default value is 4.0.

  • minimumFactorDecreaseForNextStepSize

    Minimum decrease factor in time step in subsequent iterations. The default value is 0.1.

class RungeKuttaVariableStepSizeSettingsScalarTolerances

Note

The RungeKuttaVariableStepSizeSettings class is actually a shorthand for the alias RungeKuttaVariableStepSizeSettingsScalarTolerances, for compatibility with the previous definition of the Runge-Kutta variable step-size integrator.

class RungeKuttaVariableStepSizeSettingsVectorTolerances

This class is used to define the settings for the Runge-Kutta variable step-size integration methods, where the error tolerances are defined as a vector (i.e., you could set a different absolute tolerance for position and velocity, if the propagated state is expressed in Cartesian elements). The constructor for this derived class is:

RungeKuttaVariableStepSizeSettingsVectorTolerances< TimeType, StateType >(
      simulationStartEpoch,
      initialTimeStep,
      coefficientSet,
      minimumStepSize,
      maximumStepSize,
      relativeErrorTolerance,
      absoluteErrorTolerance,
      saveFrequency,
      assessPropagationTerminationConditionDuringIntegrationSubsteps,
      safetyFactorForNextStepSize,
      maximumFactorIncreaseForNextStepSize,
      minimumFactorDecreaseForNextStepSize )

where most of the input variables are the same as for the previous constructor, except for the following:

  • StateType

    Template argument used to set the format of the state, in general Eigen::VectorXd is used. For applications where covariance propagation is also performed, this may be Eigen::MatrixXd. One can also change the precision of the state scalar, such as in Eigen::VectorXld, where long double is used instead of double.

  • relativeErrorTolerance

    StateType that defines the relative error tolerance for each state entry, for step size control of the rungeKuttaVariableStepSize numerical integrator.

  • absoluteErrorTolerance

    StateType that defines the absolute error tolerance for each state entry, for step size control of the rungeKuttaVariableStepSize numerical integrator.

class BulirschStoerIntegratorSettings

This class is used to define the settings for variable step-size integration using the Bulirsch-Stoer method. The constructor for this derived class is:

BulirschStoerIntegratorSettings< TimeType >( initialTime,
                                             initialTimeStep,
                                             extrapolationSequence,
                                             maximumNumberOfSteps,
                                             minimumStepSize,
                                             maximumStepSize,
                                             relativeErrorTolerence,
                                             absoluteErrorTolerence )

where:

  • TimeType

    Template argument used to set the precision of the time, in general double is used. For some application where a high precision is required this can be changed to e.g. long double.

  • initialTime

    TimeType that defines the simulation’s initial time. It must be a double variable-type.

  • initialTimeStep

    TimeType that defines the initial step-size to be used either by the BulirschStoerIntegrator numerical integrator. It must be a double variable-type.

  • extrapolationSequence

    ExtrapolationMethodStepSequences that defines the extrapolation sequence that is used for the BulirschStoerIntegrator numerical integrator.

  • maximumNumberOfSteps

    Number of integrations that are used for a single extrapolation. It must be a int variable-type.

  • minimumStepSize

    TimeType that defines the minimum step-size that the BulirschStoerIntegrator numerical integrator can take.

  • maximumStepSize

    TimeType that defines the maximum step-size that the BulirschStoerIntegrator numerical integrator can take.

  • relativeErrorTolerance

    TimeType that defines the relative error tolerance for step size control of the BulirschStoerIntegrator numerical integrator.

  • absoluteErrorTolerance

    TimeType that defines the absolute error tolerance for step size control of the BulirschStoerIntegrator numerical integrator.

class AdamsBashforthMoultonSettings

This class is used to define the settings for variable step-size integration using the Adams-Bashfort-Moulton method. The constructor for this derived class is:

AdamsBashforthMoultonSettings< TimeType >( initialTime,
                                           initialTimeStep,
                                           minimumStepSize,
                                           maximumStepSize,
                                           relativeErrorTolerence,
                                           absoluteErrorTolerence,
                                           minimumOrder,
                                           maximumOrder )

where:

  • TimeType

    Template argument used to set the precision of the time, in general double is used. For some application where a high precision is required this can be changed to e.g. long double.

  • initialTime

    TimeType that defines the simulation’s initial time. It must be a double variable-type.

  • initialTimeStep

    TimeType that defines the initial step-size to be used either by the AdamsBashforthMoultonIntegrator numerical integrator. It must be a double variable-type.

  • minimumStepSize

    TimeType that defines the minimum step-size that the AdamsBashforthMoultonIntegrator numerical integrator can take.

  • maximumStepSize

    TimeType that defines the maximum step-size that the AdamsBashforthMoultonIntegrator numerical integrator can take.

  • relativeErrorTolerance

    TimeType that defines the relative error tolerance for step size control of the AdamsBashforthMoultonIntegratorr numerical integrator.

  • absoluteErrorTolerance

    TimeType that defines the absolute error tolerance for step size control of the AdamsBashforthMoultonIntegrator numerical integrator.

  • minimumOrder

    The minimum order of the integrator, the default value is 6. It must be a int variable-type.

  • maximumOrder

    The maximum order of the integrator, the default value is 11. It must be a int variable-type.

Note

Aside from the arguments listed in this page, the IntegratorSettings class and derived classes described here offer a number of optional arguments. The reader is advised to examine the Doxygen documentation included in the code for further details.

Warning

Make sure that a compatible integratorType is selected, otherwise a runtime exception will be thrown.