org.opensourcephysics.numerics
Class Verlet
java.lang.Object
org.opensourcephysics.numerics.AbstractODESolver
org.opensourcephysics.numerics.Verlet
 All Implemented Interfaces:
 ODESolver
public class Verlet
 extends AbstractODESolver
Verlet: A velocity Verlet method ODE solver.
The velocity Verlet algorithm is a selfstarting 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 at 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! This implementation assumes that the state 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:
 1.1
 Author:
 Wolfgang Christian
Constructor Summary 
Verlet(ODE ode)
Constructs the velocity Verlet ODESolver for a system of ordinary differential equations. 
Method Summary 
int 
getRateCounter()
Gets the counter that records the number of times the rate has been evaluated during the current step. 
void 
initialize(double stepSize)
Initializes the ODE solver. 
double 
step()
Steps (advances) the differential equations by the stepSize. 
Methods inherited from class java.lang.Object 
clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait 
Verlet
public Verlet(ODE ode)
 Constructs the velocity Verlet ODESolver for a system of ordinary differential equations.
 Parameters:
ode
 the system of differential equations.
initialize
public void initialize(double stepSize)
 Initializes the ODE solver.
The rate array is allocated. The number of differential equations is
determined by invoking getState().length on the ODE.
 Specified by:
initialize
in interface ODESolver
 Overrides:
initialize
in class AbstractODESolver
 Parameters:
stepSize

getRateCounter
public int getRateCounter()
 Gets the counter that records the number of times the rate has been evaluated during the current step.
This method allows a model to improve its performance
by enabling the model to determine if this is the first or second time that the rate is being evaluated.
The Verlet algorithm first invokes the model's getRate method to update the position and
then again to update velocity. Because the force at the new position is computed the
second time that getRate is invoked, a model can improve its performance if it skips the force computation
during the first call to getRate.
A typical dynamics simulation should comptute the force when rateCounter is one and stores this force
for use during the next postion update.
The Verlet algorithm will perform correctly (but more slowly) if the
force is computed every time that getRate is invoked.
 Returns:
 int the counter
step
public double step()
 Steps (advances) the differential equations by the stepSize.
The ODESolver invokes the ODE's getState method to obtain the initial state of the system.
The ODESolver advances the solution and copies the new state into the
state array at the end of the solution step.
 Specified by:
step
in interface ODESolver
 Specified by:
step
in class AbstractODESolver
 Returns:
 the step size