NewGamePhysics.Mathematics.NystromIntegrator Class Reference

Nyström modification of fourth-order Runge-Kutta method of a solution of a set of ordinary second order differential equations for dynamics simulations. Works with the second derivative and must consider the first derivative as input. Based on code from Vit Buchta, June 2007. More...

List of all members.

Public Member Functions

 NystromIntegrator (ISecondDerivative secondDerivative, double timeStepsize, VectorN initialPosition, VectorN initialVelocity)
 A constructor for the Nystrom integrator object.
VectorN Reset (VectorN initialPosition, VectorN initialVelocity)
 Resets the Nystrom integrator object. Sets the time to 0 and recalculates the current acceleration.
void Step (out double newTime, out VectorN newPosition, out VectorN newVelocity, out VectorN newAcceleration)
 One step of the integration procedure. Recalculates all positions, velocities and current acceleration. Updates the time by a time step.

Detailed Description

Nyström modification of fourth-order Runge-Kutta method of a solution of a set of ordinary second order differential equations for dynamics simulations. Works with the second derivative and must consider the first derivative as input. Based on code from Vit Buchta, June 2007.

Definition at line 20 of file NystromIntegrator.cs.

Constructor & Destructor Documentation

NewGamePhysics.Mathematics.NystromIntegrator.NystromIntegrator ( ISecondDerivative  secondDerivative,
double  timeStepsize,
VectorN  initialPosition,
VectorN  initialVelocity 
)

A constructor for the Nystrom integrator object.

Parameters:
secondDerivative An object implementing the ISecondDerivative interface
timeStepsize The time step
currentPosition The vector of initial positions
currentVelocity The vector of initial velocities
initialAcceleration The vector of initial accelerations

Definition at line 60 of file NystromIntegrator.cs.

00065         {
00066             this.secondDerivative = secondDerivative;
00067             this.timeStepsize = timeStepsize;
00068             this.Reset(initialPosition, initialVelocity);
00069         }

Member Function Documentation

VectorN NewGamePhysics.Mathematics.NystromIntegrator.Reset ( VectorN  initialPosition,
VectorN  initialVelocity 
)

Resets the Nystrom integrator object. Sets the time to 0 and recalculates the current acceleration.

Parameters:
currentPosition The vector of initial positions
currentVelocity The vector of initial velocities
Returns:
The current acceleration after the reset.

Definition at line 78 of file NystromIntegrator.cs.

00081         {
00082             // Set initial conditions
00083             this.currentTime = 0.0;
00084             this.currentPosition = initialPosition;
00085             this.currentVelocity = initialVelocity;
00086 
00087             // Calculate current acceleration
00088             this.currentAcceleration = secondDerivative.GetValue(
00089                 this.currentTime, 
00090                 this.currentPosition, 
00091                 this.currentVelocity);
00092 
00093             return this.currentAcceleration;
00094         }

void NewGamePhysics.Mathematics.NystromIntegrator.Step ( out double  newTime,
out VectorN  newPosition,
out VectorN  newVelocity,
out VectorN  newAcceleration 
)

One step of the integration procedure. Recalculates all positions, velocities and current acceleration. Updates the time by a time step.

Parameters:
newTime The time at the end of the time interval
newPosition The vector of next positions
newVelocity The vector of next velocities
newAcceleration The vector of next accelerations

Definition at line 104 of file NystromIntegrator.cs.

00109         {
00110             double timeStepsizeSquared = timeStepsize * timeStepsize;
00111             double timeStepsizeHalf = timeStepsize / 2.0;
00112             VectorN k1 = currentAcceleration;
00113             VectorN k2 = secondDerivative.GetValue(currentTime + timeStepsizeHalf, currentPosition + timeStepsizeHalf * currentVelocity + timeStepsizeSquared / 8 * k1, currentVelocity + timeStepsizeHalf * k1);
00114             VectorN k3 = secondDerivative.GetValue(currentTime + timeStepsizeHalf, currentPosition + timeStepsizeHalf * currentVelocity + timeStepsizeSquared/8 * k2, currentVelocity + timeStepsizeHalf * k2);
00115             VectorN k4 = secondDerivative.GetValue(currentTime + timeStepsize,   currentPosition + timeStepsize   * currentVelocity + timeStepsizeSquared/2 * k3, currentVelocity + timeStepsize   * k3);
00116 
00117             newTime = currentTime + timeStepsize;
00118             newPosition = currentPosition + timeStepsize * currentVelocity + timeStepsizeSquared/6 * (k1 + k2 + k3);
00119             newVelocity = currentVelocity + timeStepsize/6 * (k1 + 2 * k2 + 2 * k3 + k4);
00120             newAcceleration = secondDerivative.GetValue(newTime, newPosition, newVelocity);
00121 
00122             currentTime = newTime;
00123             currentPosition = newPosition;
00124             currentVelocity = newVelocity;
00125             currentAcceleration = newAcceleration;
00126         }

The documentation for this class was generated from the following file:
Generated by  doxygen 1.6.2