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gezelter |
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#include <math.h> |
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#include "RigidBody.hpp" |
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#include "DirectionalAtom.hpp" |
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#include "simError.h" |
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#include "MatVec3.h" |
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RigidBody::RigidBody() : StuntDouble() { |
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objType = OT_RIGIDBODY; |
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} |
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RigidBody::~RigidBody() { |
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} |
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void RigidBody::addAtom(Atom* at, AtomStamp* ats) { |
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vec3 coords; |
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vec3 euler; |
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mat3x3 Atmp; |
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myAtoms.push_back(at); |
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if( !ats->havePosition() ){ |
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sprintf( painCave.errMsg, |
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"RigidBody error.\n" |
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"\tAtom %s does not have a position specified.\n" |
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"\tThis means RigidBody cannot set up reference coordinates.\n", |
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ats->getType() ); |
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painCave.isFatal = 1; |
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simError(); |
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} |
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coords[0] = ats->getPosX(); |
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coords[1] = ats->getPosY(); |
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coords[2] = ats->getPosZ(); |
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refCoords.push_back(coords); |
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if (at->isDirectional()) { |
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if( !ats->haveOrientation() ){ |
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sprintf( painCave.errMsg, |
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"RigidBody error.\n" |
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"\tAtom %s does not have an orientation specified.\n" |
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"\tThis means RigidBody cannot set up reference orientations.\n", |
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ats->getType() ); |
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painCave.isFatal = 1; |
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simError(); |
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} |
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euler[0] = ats->getEulerPhi(); |
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euler[1] = ats->getEulerTheta(); |
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euler[2] = ats->getEulerPsi(); |
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doEulerToRotMat(euler, Atmp); |
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refOrients.push_back(Atmp); |
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} |
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} |
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void RigidBody::getPos(double theP[3]){ |
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for (int i = 0; i < 3 ; i++) |
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theP[i] = pos[i]; |
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} |
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void RigidBody::setPos(double theP[3]){ |
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for (int i = 0; i < 3 ; i++) |
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pos[i] = theP[i]; |
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} |
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void RigidBody::getVel(double theV[3]){ |
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for (int i = 0; i < 3 ; i++) |
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theV[i] = vel[i]; |
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} |
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void RigidBody::setVel(double theV[3]){ |
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for (int i = 0; i < 3 ; i++) |
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vel[i] = theV[i]; |
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} |
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void RigidBody::getFrc(double theF[3]){ |
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for (int i = 0; i < 3 ; i++) |
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theF[i] = frc[i]; |
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} |
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void RigidBody::addFrc(double theF[3]){ |
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for (int i = 0; i < 3 ; i++) |
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frc[i] += theF[i]; |
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} |
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void RigidBody::zeroForces() { |
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for (int i = 0; i < 3; i++) { |
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frc[i] = 0.0; |
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trq[i] = 0.0; |
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} |
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} |
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tim |
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void RigidBody::setEuler( double phi, double theta, double psi ){ |
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gezelter |
1100 |
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A[0][0] = (cos(phi) * cos(psi)) - (sin(phi) * cos(theta) * sin(psi)); |
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A[0][1] = (sin(phi) * cos(psi)) + (cos(phi) * cos(theta) * sin(psi)); |
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A[0][2] = sin(theta) * sin(psi); |
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A[1][0] = -(cos(phi) * sin(psi)) - (sin(phi) * cos(theta) * cos(psi)); |
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A[1][1] = -(sin(phi) * sin(psi)) + (cos(phi) * cos(theta) * cos(psi)); |
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A[1][2] = sin(theta) * cos(psi); |
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A[2][0] = sin(phi) * sin(theta); |
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A[2][1] = -cos(phi) * sin(theta); |
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A[2][2] = cos(theta); |
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} |
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void RigidBody::getQ( double q[4] ){ |
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double t, s; |
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double ad1, ad2, ad3; |
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t = A[0][0] + A[1][1] + A[2][2] + 1.0; |
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if( t > 0.0 ){ |
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s = 0.5 / sqrt( t ); |
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q[0] = 0.25 / s; |
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q[1] = (A[1][2] - A[2][1]) * s; |
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q[2] = (A[2][0] - A[0][2]) * s; |
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q[3] = (A[0][1] - A[1][0]) * s; |
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} |
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else{ |
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ad1 = fabs( A[0][0] ); |
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ad2 = fabs( A[1][1] ); |
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ad3 = fabs( A[2][2] ); |
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if( ad1 >= ad2 && ad1 >= ad3 ){ |
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s = 2.0 * sqrt( 1.0 + A[0][0] - A[1][1] - A[2][2] ); |
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q[0] = (A[1][2] + A[2][1]) / s; |
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q[1] = 0.5 / s; |
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q[2] = (A[0][1] + A[1][0]) / s; |
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q[3] = (A[0][2] + A[2][0]) / s; |
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} |
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else if( ad2 >= ad1 && ad2 >= ad3 ){ |
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s = sqrt( 1.0 + A[1][1] - A[0][0] - A[2][2] ) * 2.0; |
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q[0] = (A[0][2] + A[2][0]) / s; |
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q[1] = (A[0][1] + A[1][0]) / s; |
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q[2] = 0.5 / s; |
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q[3] = (A[1][2] + A[2][1]) / s; |
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} |
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else{ |
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s = sqrt( 1.0 + A[2][2] - A[0][0] - A[1][1] ) * 2.0; |
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q[0] = (A[0][1] + A[1][0]) / s; |
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q[1] = (A[0][2] + A[2][0]) / s; |
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q[2] = (A[1][2] + A[2][1]) / s; |
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q[3] = 0.5 / s; |
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} |
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} |
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} |
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void RigidBody::setQ( double the_q[4] ){ |
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double q0Sqr, q1Sqr, q2Sqr, q3Sqr; |
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q0Sqr = the_q[0] * the_q[0]; |
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q1Sqr = the_q[1] * the_q[1]; |
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q2Sqr = the_q[2] * the_q[2]; |
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q3Sqr = the_q[3] * the_q[3]; |
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A[0][0] = q0Sqr + q1Sqr - q2Sqr - q3Sqr; |
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A[0][1] = 2.0 * ( the_q[1] * the_q[2] + the_q[0] * the_q[3] ); |
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A[0][2] = 2.0 * ( the_q[1] * the_q[3] - the_q[0] * the_q[2] ); |
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A[1][0] = 2.0 * ( the_q[1] * the_q[2] - the_q[0] * the_q[3] ); |
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A[1][1] = q0Sqr - q1Sqr + q2Sqr - q3Sqr; |
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A[1][2] = 2.0 * ( the_q[2] * the_q[3] + the_q[0] * the_q[1] ); |
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A[2][0] = 2.0 * ( the_q[1] * the_q[3] + the_q[0] * the_q[2] ); |
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A[2][1] = 2.0 * ( the_q[2] * the_q[3] - the_q[0] * the_q[1] ); |
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A[2][2] = q0Sqr - q1Sqr -q2Sqr +q3Sqr; |
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} |
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void RigidBody::getA( double the_A[3][3] ){ |
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for (int i = 0; i < 3; i++) |
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for (int j = 0; j < 3; j++) |
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tim |
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the_A[i][j] = A[i][j]; |
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gezelter |
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} |
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void RigidBody::setA( double the_A[3][3] ){ |
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for (int i = 0; i < 3; i++) |
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for (int j = 0; j < 3; j++) |
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A[i][j] = the_A[i][j]; |
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} |
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void RigidBody::getJ( double theJ[3] ){ |
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for (int i = 0; i < 3; i++) |
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theJ[i] = ji[i]; |
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} |
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void RigidBody::setJ( double theJ[3] ){ |
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for (int i = 0; i < 3; i++) |
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ji[i] = theJ[i]; |
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} |
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void RigidBody::getTrq(double theT[3]){ |
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for (int i = 0; i < 3 ; i++) |
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theT[i] = trq[i]; |
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} |
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void RigidBody::addTrq(double theT[3]){ |
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for (int i = 0; i < 3 ; i++) |
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trq[i] += theT[i]; |
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} |
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void RigidBody::getI( double the_I[3][3] ){ |
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for (int i = 0; i < 3; i++) |
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for (int j = 0; j < 3; j++) |
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the_I[i][j] = I[i][j]; |
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} |
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void RigidBody::lab2Body( double r[3] ){ |
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double rl[3]; // the lab frame vector |
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rl[0] = r[0]; |
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rl[1] = r[1]; |
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rl[2] = r[2]; |
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r[0] = (A[0][0] * rl[0]) + (A[0][1] * rl[1]) + (A[0][2] * rl[2]); |
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r[1] = (A[1][0] * rl[0]) + (A[1][1] * rl[1]) + (A[1][2] * rl[2]); |
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r[2] = (A[2][0] * rl[0]) + (A[2][1] * rl[1]) + (A[2][2] * rl[2]); |
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} |
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void RigidBody::body2Lab( double r[3] ){ |
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double rb[3]; // the body frame vector |
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rb[0] = r[0]; |
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rb[1] = r[1]; |
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rb[2] = r[2]; |
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r[0] = (A[0][0] * rb[0]) + (A[1][0] * rb[1]) + (A[2][0] * rb[2]); |
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r[1] = (A[0][1] * rb[0]) + (A[1][1] * rb[1]) + (A[2][1] * rb[2]); |
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r[2] = (A[0][2] * rb[0]) + (A[1][2] * rb[1]) + (A[2][2] * rb[2]); |
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} |
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void RigidBody::calcRefCoords( ) { |
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tim |
1113 |
int i,j,k, it; |
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gezelter |
1100 |
double mtmp; |
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vec3 apos; |
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double refCOM[3]; |
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tim |
1113 |
vec3 ptmp; |
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double Itmp[3][3]; |
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double evals[3]; |
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double evects[3][3]; |
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double r, r2, len; |
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gezelter |
1100 |
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tim |
1113 |
// First, find the center of mass: |
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gezelter |
1100 |
mass = 0.0; |
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for (j=0; j<3; j++) |
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refCOM[j] = 0.0; |
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for (i = 0; i < myAtoms.size(); i++) { |
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mtmp = myAtoms[i]->getMass(); |
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mass += mtmp; |
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apos = refCoords[i]; |
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for(j = 0; j < 3; j++) { |
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refCOM[j] += apos[j]*mtmp; |
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} |
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} |
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for(j = 0; j < 3; j++) |
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refCOM[j] /= mass; |
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tim |
1113 |
// Next, move the origin of the reference coordinate system to the COM: |
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gezelter |
1100 |
for (i = 0; i < myAtoms.size(); i++) { |
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apos = refCoords[i]; |
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for (j=0; j < 3; j++) { |
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apos[j] = apos[j] - refCOM[j]; |
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} |
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refCoords[i] = apos; |
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} |
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tim |
1113 |
// Moment of Inertia calculation |
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for (i = 0; i < 3; i++) |
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for (j = 0; j < 3; j++) |
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Itmp[i][j] = 0.0; |
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for (it = 0; it < myAtoms.size(); it++) { |
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mtmp = myAtoms[it]->getMass(); |
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ptmp = refCoords[it]; |
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r= norm3(ptmp.vec); |
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r2 = r*r; |
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for (i = 0; i < 3; i++) { |
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for (j = 0; j < 3; j++) { |
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if (i==j) Itmp[i][j] += mtmp * r2; |
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Itmp[i][j] -= mtmp * ptmp.vec[i]*ptmp.vec[j]; |
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} |
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} |
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} |
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diagonalize3x3(Itmp, evals, sU); |
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// zero out I and then fill the diagonals with the moments of inertia: |
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for (i = 0; i < 3; i++) { |
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for (j = 0; j < 3; j++) { |
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I[i][j] = 0.0; |
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} |
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I[i][i] = evals[i]; |
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} |
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// renormalize column vectors: |
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for (i=0; i < 3; i++) { |
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len = 0.0; |
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for (j = 0; j < 3; j++) { |
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len += sU[i][j]*sU[i][j]; |
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} |
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len = sqrt(len); |
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for (j = 0; j < 3; j++) { |
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sU[i][j] /= len; |
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} |
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} |
350 |
gezelter |
1100 |
} |
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void RigidBody::doEulerToRotMat(vec3 &euler, mat3x3 &myA ){ |
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double phi, theta, psi; |
355 |
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356 |
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phi = euler[0]; |
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theta = euler[1]; |
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psi = euler[2]; |
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360 |
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myA[0][0] = (cos(phi) * cos(psi)) - (sin(phi) * cos(theta) * sin(psi)); |
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myA[0][1] = (sin(phi) * cos(psi)) + (cos(phi) * cos(theta) * sin(psi)); |
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myA[0][2] = sin(theta) * sin(psi); |
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myA[1][0] = -(cos(phi) * sin(psi)) - (sin(phi) * cos(theta) * cos(psi)); |
365 |
|
|
myA[1][1] = -(sin(phi) * sin(psi)) + (cos(phi) * cos(theta) * cos(psi)); |
366 |
|
|
myA[1][2] = sin(theta) * cos(psi); |
367 |
|
|
|
368 |
|
|
myA[2][0] = sin(phi) * sin(theta); |
369 |
|
|
myA[2][1] = -cos(phi) * sin(theta); |
370 |
|
|
myA[2][2] = cos(theta); |
371 |
|
|
|
372 |
|
|
} |
373 |
|
|
|
374 |
|
|
void RigidBody::calcForcesAndTorques() { |
375 |
|
|
|
376 |
|
|
// Convert Atomic forces and torques to total forces and torques: |
377 |
|
|
int i, j; |
378 |
|
|
double apos[3]; |
379 |
|
|
double afrc[3]; |
380 |
|
|
double atrq[3]; |
381 |
|
|
double rpos[3]; |
382 |
|
|
|
383 |
|
|
zeroForces(); |
384 |
|
|
|
385 |
|
|
for (i = 0; i < myAtoms.size(); i++) { |
386 |
|
|
|
387 |
|
|
myAtoms[i]->getPos(apos); |
388 |
|
|
myAtoms[i]->getFrc(afrc); |
389 |
|
|
|
390 |
|
|
for (j=0; j<3; j++) { |
391 |
|
|
rpos[j] = apos[j] - pos[j]; |
392 |
|
|
frc[j] += afrc[j]; |
393 |
|
|
} |
394 |
|
|
|
395 |
|
|
trq[0] += rpos[1]*afrc[2] - rpos[2]*afrc[1]; |
396 |
|
|
trq[1] += rpos[2]*afrc[0] - rpos[0]*afrc[2]; |
397 |
|
|
trq[2] += rpos[0]*afrc[1] - rpos[1]*afrc[0]; |
398 |
|
|
|
399 |
|
|
// If the atom has a torque associated with it, then we also need to |
400 |
|
|
// migrate the torques onto the center of mass: |
401 |
|
|
|
402 |
|
|
if (myAtoms[i]->isDirectional()) { |
403 |
|
|
|
404 |
|
|
myAtoms[i]->getTrq(atrq); |
405 |
|
|
|
406 |
|
|
for (j=0; j<3; j++) |
407 |
|
|
trq[j] += atrq[j]; |
408 |
|
|
} |
409 |
|
|
} |
410 |
|
|
|
411 |
|
|
// Convert Torque to Body-fixed coordinates: |
412 |
|
|
// (Actually, on second thought, don't. Integrator does this now.) |
413 |
|
|
// lab2Body(trq); |
414 |
|
|
|
415 |
|
|
} |
416 |
|
|
|
417 |
|
|
void RigidBody::updateAtoms() { |
418 |
|
|
int i, j; |
419 |
|
|
vec3 ref; |
420 |
|
|
double apos[3]; |
421 |
|
|
DirectionalAtom* dAtom; |
422 |
|
|
|
423 |
|
|
for (i = 0; i < myAtoms.size(); i++) { |
424 |
|
|
|
425 |
|
|
ref = refCoords[i]; |
426 |
|
|
|
427 |
|
|
body2Lab(ref.vec); |
428 |
|
|
|
429 |
|
|
for (j = 0; j<3; j++) |
430 |
|
|
apos[j] = pos[j] + ref.vec[j]; |
431 |
|
|
|
432 |
|
|
myAtoms[i]->setPos(apos); |
433 |
|
|
|
434 |
|
|
if (myAtoms[i]->isDirectional()) { |
435 |
|
|
|
436 |
|
|
dAtom = (DirectionalAtom *) myAtoms[i]; |
437 |
|
|
dAtom->rotateBy( A ); |
438 |
|
|
|
439 |
|
|
} |
440 |
|
|
} |
441 |
|
|
} |
442 |
|
|
|
443 |
|
|
void RigidBody::getGrad( double grad[6] ) { |
444 |
|
|
|
445 |
|
|
double myEuler[3]; |
446 |
|
|
double phi, theta, psi; |
447 |
|
|
double cphi, sphi, ctheta, stheta; |
448 |
|
|
double ephi[3]; |
449 |
|
|
double etheta[3]; |
450 |
|
|
double epsi[3]; |
451 |
|
|
|
452 |
|
|
this->getEulerAngles(myEuler); |
453 |
|
|
|
454 |
|
|
phi = myEuler[0]; |
455 |
|
|
theta = myEuler[1]; |
456 |
|
|
psi = myEuler[2]; |
457 |
|
|
|
458 |
|
|
cphi = cos(phi); |
459 |
|
|
sphi = sin(phi); |
460 |
|
|
ctheta = cos(theta); |
461 |
|
|
stheta = sin(theta); |
462 |
|
|
|
463 |
|
|
// get unit vectors along the phi, theta and psi rotation axes |
464 |
|
|
|
465 |
|
|
ephi[0] = 0.0; |
466 |
|
|
ephi[1] = 0.0; |
467 |
|
|
ephi[2] = 1.0; |
468 |
|
|
|
469 |
|
|
etheta[0] = cphi; |
470 |
|
|
etheta[1] = sphi; |
471 |
|
|
etheta[2] = 0.0; |
472 |
|
|
|
473 |
|
|
epsi[0] = stheta * cphi; |
474 |
|
|
epsi[1] = stheta * sphi; |
475 |
|
|
epsi[2] = ctheta; |
476 |
|
|
|
477 |
|
|
for (int j = 0 ; j<3; j++) |
478 |
|
|
grad[j] = frc[j]; |
479 |
|
|
|
480 |
|
|
grad[3] = 0.0; |
481 |
|
|
grad[4] = 0.0; |
482 |
|
|
grad[5] = 0.0; |
483 |
|
|
|
484 |
|
|
for (int j = 0; j < 3; j++ ) { |
485 |
|
|
|
486 |
|
|
grad[3] += trq[j]*ephi[j]; |
487 |
|
|
grad[4] += trq[j]*etheta[j]; |
488 |
|
|
grad[5] += trq[j]*epsi[j]; |
489 |
|
|
|
490 |
|
|
} |
491 |
|
|
|
492 |
|
|
} |
493 |
|
|
|
494 |
|
|
/** |
495 |
|
|
* getEulerAngles computes a set of Euler angle values consistent |
496 |
|
|
* with an input rotation matrix. They are returned in the following |
497 |
|
|
* order: |
498 |
|
|
* myEuler[0] = phi; |
499 |
|
|
* myEuler[1] = theta; |
500 |
|
|
* myEuler[2] = psi; |
501 |
|
|
*/ |
502 |
|
|
void RigidBody::getEulerAngles(double myEuler[3]) { |
503 |
|
|
|
504 |
|
|
// We use so-called "x-convention", which is the most common |
505 |
|
|
// definition. In this convention, the rotation given by Euler |
506 |
|
|
// angles (phi, theta, psi), where the first rotation is by an angle |
507 |
|
|
// phi about the z-axis, the second is by an angle theta (0 <= theta |
508 |
|
|
// <= 180) about the x-axis, and the third is by an angle psi about |
509 |
|
|
// the z-axis (again). |
510 |
|
|
|
511 |
|
|
|
512 |
|
|
double phi,theta,psi,eps; |
513 |
|
|
double pi; |
514 |
|
|
double cphi,ctheta,cpsi; |
515 |
|
|
double sphi,stheta,spsi; |
516 |
|
|
double b[3]; |
517 |
|
|
int flip[3]; |
518 |
|
|
|
519 |
|
|
// set the tolerance for Euler angles and rotation elements |
520 |
|
|
|
521 |
|
|
eps = 1.0e-8; |
522 |
|
|
|
523 |
|
|
theta = acos(min(1.0,max(-1.0,A[2][2]))); |
524 |
|
|
ctheta = A[2][2]; |
525 |
|
|
stheta = sqrt(1.0 - ctheta * ctheta); |
526 |
|
|
|
527 |
|
|
// when sin(theta) is close to 0, we need to consider the |
528 |
|
|
// possibility of a singularity. In this case, we can assign an |
529 |
|
|
// arbitary value to phi (or psi), and then determine the psi (or |
530 |
|
|
// phi) or vice-versa. We'll assume that phi always gets the |
531 |
|
|
// rotation, and psi is 0 in cases of singularity. we use atan2 |
532 |
|
|
// instead of atan, since atan2 will give us -Pi to Pi. Since 0 <= |
533 |
|
|
// theta <= 180, sin(theta) will be always non-negative. Therefore, |
534 |
|
|
// it never changes the sign of both of the parameters passed to |
535 |
|
|
// atan2. |
536 |
|
|
|
537 |
|
|
if (fabs(stheta) <= eps){ |
538 |
|
|
psi = 0.0; |
539 |
|
|
phi = atan2(-A[1][0], A[0][0]); |
540 |
|
|
} |
541 |
|
|
// we only have one unique solution |
542 |
|
|
else{ |
543 |
|
|
phi = atan2(A[2][0], -A[2][1]); |
544 |
|
|
psi = atan2(A[0][2], A[1][2]); |
545 |
|
|
} |
546 |
|
|
|
547 |
|
|
//wrap phi and psi, make sure they are in the range from 0 to 2*Pi |
548 |
|
|
//if (phi < 0) |
549 |
|
|
// phi += M_PI; |
550 |
|
|
|
551 |
|
|
//if (psi < 0) |
552 |
|
|
// psi += M_PI; |
553 |
|
|
|
554 |
|
|
myEuler[0] = phi; |
555 |
|
|
myEuler[1] = theta; |
556 |
|
|
myEuler[2] = psi; |
557 |
|
|
|
558 |
|
|
return; |
559 |
|
|
} |
560 |
|
|
|
561 |
|
|
double RigidBody::max(double x, double y) { |
562 |
|
|
return (x > y) ? x : y; |
563 |
|
|
} |
564 |
|
|
|
565 |
|
|
double RigidBody::min(double x, double y) { |
566 |
|
|
return (x > y) ? y : x; |
567 |
|
|
} |
568 |
|
|
|
569 |
|
|
void RigidBody::findCOM() { |
570 |
|
|
|
571 |
|
|
size_t i; |
572 |
|
|
int j; |
573 |
|
|
double mtmp; |
574 |
|
|
double ptmp[3]; |
575 |
|
|
double vtmp[3]; |
576 |
|
|
|
577 |
|
|
for(j = 0; j < 3; j++) { |
578 |
|
|
pos[j] = 0.0; |
579 |
|
|
vel[j] = 0.0; |
580 |
|
|
} |
581 |
|
|
mass = 0.0; |
582 |
|
|
|
583 |
|
|
for (i = 0; i < myAtoms.size(); i++) { |
584 |
|
|
|
585 |
|
|
mtmp = myAtoms[i]->getMass(); |
586 |
|
|
myAtoms[i]->getPos(ptmp); |
587 |
|
|
myAtoms[i]->getVel(vtmp); |
588 |
|
|
|
589 |
|
|
mass += mtmp; |
590 |
|
|
|
591 |
|
|
for(j = 0; j < 3; j++) { |
592 |
|
|
pos[j] += ptmp[j]*mtmp; |
593 |
|
|
vel[j] += vtmp[j]*mtmp; |
594 |
|
|
} |
595 |
|
|
|
596 |
|
|
} |
597 |
|
|
|
598 |
|
|
for(j = 0; j < 3; j++) { |
599 |
|
|
pos[j] /= mass; |
600 |
|
|
vel[j] /= mass; |
601 |
|
|
} |
602 |
|
|
|
603 |
|
|
} |