//----------------------------------------------------------------------------
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::Initialize (double time, double deltaTime, double radius,
double theta, double radiusDot, double thetaDot)
{
mTime = time;
mDeltaTime = deltaTime;
// state variables
mState[0] = theta;
mState[1] = thetaDot;
mState[2] = radius;
mState[3] = radiusDot;
// Compute c0 and c1 in the potential energy function V(theta).
double gm = Gravity*Mass;
double gm2 = gm*Mass;
double radiusSqr = radius*radius;
double alpha = Mass*radiusSqr*thetaDot;
double g2m4da2 = gm2*gm2/(alpha*alpha);
double v0 = -gm/radius;
double dv0 = gm2*radiusDot/alpha;
double v0Plus = v0 + g2m4da2;
double sinTheta0 = Mathd::Sin(theta);
double cosTheta0 = Mathd::Cos(theta);
double c0 = v0Plus*sinTheta0 + dv0*cosTheta0;
double c1 = v0Plus*cosTheta0 - dv0*sinTheta0;
// Auxiliary variables needed by function DTheta(...).
mAux[0] = c0;
mAux[1] = c1;
mAux[2] = g2m4da2;
mAux[3] = alpha/(gm*gm2);
// ellipse parameters
double gamma0 = radiusSqr*Mathd::FAbs(thetaDot);
double tmp0 = radiusSqr*radius*thetaDot*thetaDot - gm;
double tmp1 = radiusSqr*radiusDot*thetaDot;
double gamma1 = Mathd::Sqrt(tmp0*tmp0 + tmp1*tmp1);
mEccentricity = gamma1/gm;
mRho = gamma0*gamma0/gamma1;
double tmp2 = 1.0 - mEccentricity*mEccentricity;
assertion(tmp2 > 0.0, "Invalid eccentricity.\n");
mMajorAxis = mRho*mEccentricity/tmp2;
mMinorAxis = mMajorAxis*Mathd::Sqrt(tmp2);
// 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(1, mDeltaTime, OdeFunction, mAux);
}
//----------------------------------------------------------------------------
void PhysicsModule::Initialize (double time, double deltaTime, double theta,
double thetaDot)
{
mTime = time;
mDeltaTime = deltaTime;
// state variables
mState[0] = theta;
mState[1] = thetaDot;
// auxiliary variables
mAux[0] = GDivL;
mAux[1] = CDivM;
// 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(2, mDeltaTime, OdeFunction, mAux);
}
//----------------------------------------------------------------------------
void PhysicsModule::Initialize (double time, double deltaTime, double x,
double w, double xDer, double wDer)
{
mTime = time;
mDeltaTime = deltaTime;
// state variables
mState[0] = x;
mState[1] = xDer;
mState[2] = w;
mState[3] = wDer;
// auxiliary variables
mAux[0] = Friction/Mass;
mAux[1] = Gravity*Mathd::Sin(Angle);
// RK4 differential equation solver. Since m_pkSolver 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);
}
//----------------------------------------------------------------------------
void PhysicsModule::Initialize (double time, double deltaTime, double theta,
double phi, double thetaDot, double phiDot)
{
mTime = time;
mDeltaTime = deltaTime;
// state variables
mState[0] = theta;
mState[1] = thetaDot;
mState[2] = phi;
mState[3] = phiDot;
// auxiliary variables
mAux[0] = AngularSpeed*Mathd::Sin(Latitude); // w*sin(lat)
mAux[1] = AngularSpeed*Mathd::Cos(Latitude); // w*cos(lat)
mAux[2] = GDivL;
// 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);
}
//----------------------------------------------------------------------------
void PhysicsModule::Initialize (double time, double deltaTime, double y1,
double y2, double y1Dot, double y2Dot)
{
mTime = time;
mDeltaTime = deltaTime;
// state variables
mState[0] = y1; // y1(0)
mState[1] = y1Dot; // y1'(0)
mState[2] = y2; // y2(0)
mState[3] = y2Dot; // y2'(0)
// auxiliary variables
mAux[0] = A1*A1; // a1^2
mAux[1] = A2*A2; // a2^2
mAux[2] = Gravity; // g
// 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);
}