SimTK::VerletIntegrator Class Reference

This is an Integrator based on the velocity Verlet algorithm. More...

#include <VerletIntegrator.h>

Inheritance diagram for SimTK::VerletIntegrator:

List of all members.

Public Member Functions
	VerletIntegrator (const System &sys)
	Create a VerletIntegrator for integrating a System with variable size steps.
	VerletIntegrator (const System &sys, Real stepSize)
	Create a VerletIntegrator for integrating a System with fixed size steps.
	~VerletIntegrator ()

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Detailed Description

This is an Integrator based on the velocity Verlet algorithm.

It is a third order, semi-explicit integrator. Velocity independent forces only need to be evaluated once per time step, but forces which depend on velocity must be evaluated multiple times. This makes it a very efficient algorithm for systems where most of the time is spent evaluating forces that depend only on position.

Although this is a third order integrator, the velocities reported at each time step are only accurate to lower order. If any forces depend on velocity, this may lead to a reduction in the overall accuracy of integration, since the forces being integrated are less accurate than the method used to integrate them. Whether this actually happens in a particular case depends on the magnitude of the velocity dependent forces, how sensitive they are to errors in velocity, and how the system is affected by those forces.

When this integrator is used with fixed size time steps, it is symplectic. This means that it is extremely good at conserving energy, and will usually produce much less variation in energy than most other integrators would at the same step size. This makes it a good choice for problems where accurate energy conservation over long time periods is important. To use it in this way, use the constructor which takes a step size, or call setFixedStepSize().

Alternatively, it may be used in variable step mode, in which case the step size is selected based on the accuracy specified by calling setAccuracy(). In this case it is no longer symplectic, so the energy will fluctuate more over time. Because the step size is adjusted based on the local error in each step, however, the trajectory will generally be more accurate in variable step size mode than would be obtained with the same number of fixed size steps spanning the same amount of time.

Another possible strategy is to set only a maximum step size but not a minimum step size. It should be chosen such that most time steps will use the fixed maximum step size, but smaller steps can be used when necessary to preserve accuracy. This leads to fairly good long term energy conservation, while still maintaining reasonable accuracy when unusually large forces transiently occur.

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Constructor & Destructor Documentation

SimTK::VerletIntegrator::VerletIntegrator

(

const System &

sys

)

[explicit]

Create a VerletIntegrator for integrating a System with variable size steps.

SimTK::VerletIntegrator::VerletIntegrator	(	const System &	sys,
		Real	stepSize
	)

Create a VerletIntegrator for integrating a System with fixed size steps.

SimTK::VerletIntegrator::~VerletIntegrator

(

)

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The documentation for this class was generated from the following file:

• VerletIntegrator.h