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// Geometric Tools, LLC
// Copyright (c) 1998-2014
// Distributed under the Boost Software License, Version 1.0.
// http://www.boost.org/LICENSE_1_0.txt
// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt
//
// File Version: 5.0.0 (2010/01/01)
#include "PhysicsModule.h"
#include "Wm5Math.h"
#include "Wm5Memory.h"
#include "Wm5OdeRungeKutta4.h"
//----------------------------------------------------------------------------
PhysicsModule::PhysicsModule ()
:
Mu(0.0),
Gravity(0.0),
Angle(0.0),
SinAngle(0.0),
CosAngle(0.0),
XLocExt(0.0),
YLocExt(0.0),
ZLocExt(0.0),
mTime(0.0),
mDeltaTime(0.0),
mSolver(0)
{
mState[0] = 0.0;
mState[1] = 0.0;
mState[2] = 0.0;
mState[3] = 0.0;
mState[4] = 0.0;
mState[5] = 0.0;
mAux[0] = 0.0;
mAux[1] = 0.0;
}
//----------------------------------------------------------------------------
PhysicsModule::~PhysicsModule ()
{
delete0(mSolver);
}
//----------------------------------------------------------------------------
void PhysicsModule::Initialize (double time, double deltaTime, double x,
double w, double theta, double xDot, double wDot, double thetaDot)
{
mTime = time;
mDeltaTime = deltaTime;
// state variables
mState[0] = x;
mState[1] = xDot;
mState[2] = w;
mState[3] = wDot;
mState[4] = theta;
mState[5] = thetaDot;
// auxiliary variables
SinAngle = Mathd::Sin(Angle);
CosAngle = Mathd::Cos(Angle);
mAux[0] = Mu*Gravity; // c/m in the one-particle system example
mAux[1] = Gravity*SinAngle;
// RK4 differential equation solver. Since mSolver is a base class
// pointer, you can instead create a solver of whatever class you prefer.
delete0(mSolver);
mSolver = new0 OdeRungeKutta4d(4, mDeltaTime, OdeFunction, mAux);
// Set up for angular speed.
mTheta0 = theta;
mThetaDer0 = thetaDot;
double xx = XLocExt*XLocExt;
double xy = XLocExt*YLocExt;
double yy = YLocExt*YLocExt;
double tmp1 = xx + yy;
double tmp2 = Mathd::Sqrt(tmp1);
double tmp3 = 4.0*xy/3.0;
double tmp4 = 0.5*Mathd::Log((tmp2 + XLocExt)/(tmp2 - XLocExt));
double tmp5 = 0.5*Mathd::Log((tmp2 + YLocExt)/(tmp2 - YLocExt));
double numer = tmp3*tmp2 + XLocExt*xx*tmp5 + YLocExt*yy*tmp4;
double denom = tmp3*tmp1;
double coeff = Mu*Gravity*numer/denom;
double angSpeed = Mathd::FAbs(thetaDot);
if (angSpeed > Mathd::ZERO_TOLERANCE)
{
mAngVelCoeff = coeff/angSpeed;
}
else
{
mAngVelCoeff = 0.0;
}
}
//----------------------------------------------------------------------------
void PhysicsModule::GetRectangle (double& x00, double& y00, double& x10,
double& y10, double& x11, double& y11, double& x01, double& y01) const
{
// P = (x,y) + sx*XLocExt*(cos(A),sin(A)) + sy*YLocExt*(-sin(A),cos(A))
// where |sx| = 1 and |sy| = 1 (four choices on sign)
double cs = Mathd::Cos(mState[4]);
double sn = Mathd::Sin(mState[4]);
// sx = -1, sy = -1
x00 = mState[0] - XLocExt*cs + YLocExt*sn;
y00 = mState[2] - XLocExt*sn - YLocExt*cs;
// sx = +1, sy = -1
x10 = mState[0] + XLocExt*cs + YLocExt*sn;
y10 = mState[2] + XLocExt*sn - YLocExt*cs;
// sx = +1, sy = +1
x11 = mState[0] + XLocExt*cs - YLocExt*sn;
y11 = mState[2] + XLocExt*sn + YLocExt*cs;
// sx = -1, sy = +1
x01 = mState[0] - XLocExt*cs - YLocExt*sn;
y01 = mState[2] - XLocExt*sn + YLocExt*cs;
}
//----------------------------------------------------------------------------
void PhysicsModule::Update ()
{
if (mSolver)
{
// Apply a single step of the ODE solver.
mSolver->Update(mTime, mState, mTime, mState);
// Update for angular speed.
double angTmp = mAngVelCoeff*mTime;
double angVelMult = 1.0 - angTmp;
if (angVelMult > 0.0)
{
mState[5] = angVelMult*mThetaDer0;
mState[4] = mTheta0 + mTime*(1.0 - 0.5*angTmp)*mThetaDer0;
}
else
{
mState[5] = 0.0;
}
}
}
//----------------------------------------------------------------------------
void PhysicsModule::OdeFunction (double, const double* state, void* data,
double* output)
{
double* aux = (double*)data;
double vLen = Mathd::Sqrt(state[1]*state[1] + state[3]*state[3]);
double xDotFunction, wDotFunction;
if (vLen > Mathd::ZERO_TOLERANCE)
{
double temp = -aux[0]/vLen;
xDotFunction = temp*state[1];
wDotFunction = temp*state[3] - aux[1];
}
else
{
// Velocity is effectively zero, so frictional force is zero.
xDotFunction = 0.0;
wDotFunction = -aux[1];
}
// x function
output[0] = state[1];
// dot(x) function
output[1] = xDotFunction;
// w function
output[2] = state[3];
// dot(w) function
output[3] = wDotFunction;
}
//----------------------------------------------------------------------------
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