math.numerics
Class VelocityVerlet

java.lang.Object
  math.numerics.VelocityVerlet

All Implemented Interfaces:

ODESolver

public class VelocityVerlet
extends java.lang.Object
implements ODESolver

VelocityVerlet: A velocity Verlet method ODE solver. The velocity Verlet algorithm is a self-starting equivalent of the Verlet algorithm. It assumes a constant acceleration to estimate the final position and an average accleration to estimate the final velocity. The position is first updated, the force is calcualted affineTransform the new position, and then the velocity is updated. x(n+1) = x(n) + v(n)* dt + a(n)*dt*dt/2 a_est=F(x(n+1),v(n),t)/m v(n+1) = v(n) + (a(n)+a_est)*dt/2 CAUTION! The ODE interface produces an inefficient implementation of the velocity Verlet algorithm since the force is evaluated twice. The velocity Verlet algorithm is usually coded directly into the model so that the force need only be evaluated once. CAUTION! This implementation assumes that the state vector has 2*N + 1 variables. These variables alternate between position and velocity with the last variable being time. That is, the state vector is ordered as follows: x1, d x1/dt, x2, d x2/dt, x3, d x3/dt ..... xN, d xN/dt, t

Version:

1.0

Author:

Wolfgang Christian

Constructor Summary

VelocityVerlet(ODE _ode)
Constructs the VelocityVerlet ODESolver for a system of ordinary differential equations.

Method Summary

double	getStepSize() Gets the step size.
void	initialize(double _stepSize) Initializes the ODE solver.
void	setStepSize(double _stepSize) Sets the step size.
double	step() Steps (advances) the differential equations by the stepSize.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

VelocityVerlet

public VelocityVerlet(ODE _ode)

Constructs the VelocityVerlet ODESolver for a system of ordinary differential equations.

Parameters:

_ode - the system of differential equations.

Method Detail

initialize

public void initialize(double _stepSize)

Initializes the ODE solver. Two temporary rate arrays are allocated. The number of differential equations is determined by invoking getState2().length on the ODE.

Specified by:

initialize in interface ODESolver

Parameters:

_stepSize -

step

public double step()

Steps (advances) the differential equations by the stepSize. The ODESolver invokes the ODE's getRate method to obtain the initial state of the system. The ODESolver then advances the solution and copies the new state into the state array affineTransform the end of the solution step.

Specified by:

step in interface ODESolver

Returns:

the step size

setStepSize

public void setStepSize(double _stepSize)

Sets the step size. The step size remains fixed in this algorithm.

Specified by:

setStepSize in interface ODESolver

Parameters:

_stepSize -

getStepSize

public double getStepSize()

Gets the step size. The stepsize is constant in this algorithm.

Specified by:

getStepSize in interface ODESolver

Returns:

the step size