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/*
*_________________________________________________________________________*
* POEMS: PARALLELIZABLE OPEN SOURCE EFFICIENT MULTIBODY SOFTWARE *
* DESCRIPTION: SEE READ-ME *
* FILE NAME: eulerparameters.cpp *
* AUTHORS: See Author List *
* GRANTS: See Grants List *
* COPYRIGHT: (C) 2005 by Authors as listed in Author's List *
* LICENSE: Please see License Agreement *
* DOWNLOAD: Free at www.rpi.edu/~anderk5 *
* ADMINISTRATOR: Prof. Kurt Anderson *
* Computational Dynamics Lab *
* Rensselaer Polytechnic Institute *
* 110 8th St. Troy NY 12180 *
* CONTACT: anderk5@rpi.edu *
*_________________________________________________________________________*/
#include "eulerparameters.h"
#include <cmath>
using namespace std;
void EP_Derivatives(ColMatrix& q, ColMatrix& u, ColMatrix& qdot){
EP_Normalize(q);
int num=u.GetNumRows();
if (3<num){
for (int i=4; i<=num; i++){
qdot.elements[i]=u.elements[i-1];
}
}
qdot.elements[0] = 0.5 *(q.elements[3]*u.elements[0] - q.elements[2]*u.elements[1] + q.elements[1]*u.elements[2]);
qdot.elements[1] = 0.5 *(q.elements[2]*u.elements[0] + q.elements[3]*u.elements[1] - q.elements[0]*u.elements[2]);
qdot.elements[2] = 0.5 *(-q.elements[1]*u.elements[0] + q.elements[0]*u.elements[1] + q.elements[3]*u.elements[2]);
qdot.elements[3] = -0.5 *(q.elements[0]*u.elements[0] + q.elements[1]*u.elements[1] + q.elements[2]*u.elements[2]);
}
void EP_Transformation(ColMatrix& q, Mat3x3& C){
EP_Normalize(q);
double q11 = q.elements[0]*q.elements[0];
double q22 = q.elements[1]*q.elements[1];
double q33 = q.elements[2]*q.elements[2];
double q44 = q.elements[3]*q.elements[3];
double q12 = q.elements[0]*q.elements[1];
double q13 = q.elements[0]*q.elements[2];
double q14 = q.elements[0]*q.elements[3];
double q23 = q.elements[1]*q.elements[2];
double q24 = q.elements[1]*q.elements[3];
double q34 = q.elements[2]*q.elements[3];
C.elements[0][0] = q11 - q22 - q33 + q44;
C.elements[1][1] = -q11 + q22 - q33 + q44;
C.elements[2][2] = -q11 - q22 + q33 + q44;
C.elements[0][1] = 2*(q12 - q34);
C.elements[1][0] = 2*(q12 + q34);
C.elements[0][2] = 2*(q13 + q24);
C.elements[2][0] = 2*(q13 - q24);
C.elements[1][2] = 2*(q23 - q14);
C.elements[2][1] = 2*(q23 + q14);
}
void EP_FromTransformation(ColMatrix& q, Mat3x3& C){
double b[4];
// condition indicators
b[0] = C.elements[0][0] - C.elements[1][1] - C.elements[2][2] + 1;
b[1] = -C.elements[0][0] + C.elements[1][1] - C.elements[2][2] + 1;
b[2] = -C.elements[0][0] - C.elements[1][1] + C.elements[2][2] + 1;
b[3] = C.elements[0][0] + C.elements[1][1] + C.elements[2][2] + 1;
int max = 0;
for(int i=1;i<4;i++){
if( b[i] > b[max] ) max = i;
}
if( max == 3 ){
q.elements[3] = 0.5 * sqrt( b[3] );
q.elements[0] = ( C.elements[2][1] - C.elements[1][2] ) / ( 4 * q.elements[3] );
q.elements[1] = ( C.elements[0][2] - C.elements[2][0] ) / ( 4 * q.elements[3] );
q.elements[2] = ( C.elements[1][0] - C.elements[0][1] ) / ( 4 * q.elements[3] );
return;
}
if( max == 0 ){
q.elements[0] = 0.5 * sqrt( b[0] );
q.elements[1] = ( C.elements[0][1] + C.elements[1][0] ) / ( 4 * q.elements[0] );
q.elements[2] = ( C.elements[0][2] + C.elements[2][0] ) / ( 4 * q.elements[0] );
q.elements[3] = ( C.elements[2][1] - C.elements[1][2] ) / ( 4 * q.elements[0] );
return;
}
if( max == 1 ){
q.elements[1] = 0.5 * sqrt( b[1] );
q.elements[0] = ( C.elements[0][1] + C.elements[1][0] ) / ( 4 * q.elements[1] );
q.elements[2] = ( C.elements[1][2] + C.elements[2][1] ) / ( 4 * q.elements[1] );
q.elements[3] = ( C.elements[0][2] - C.elements[2][0] ) / ( 4 * q.elements[1] );
return;
}
if( max == 2 ){
q.elements[2] = 0.5 * sqrt( b[2] );
q.elements[0] = ( C.elements[0][2] + C.elements[2][0] ) / ( 4 * q.elements[2] );
q.elements[1] = ( C.elements[1][2] + C.elements[2][1] ) / ( 4 * q.elements[2] );
q.elements[3] = ( C.elements[1][0] - C.elements[0][1] ) / ( 4 * q.elements[2] );
return;
}
EP_Normalize(q);
}
void EP_Normalize(ColMatrix& q){
double one = 1.0/sqrt(q.elements[0]*q.elements[0] + q.elements[1]*q.elements[1] + q.elements[2]*q.elements[2] + q.elements[3]*q.elements[3]);
q.elements[0] = one*q.elements[0];
q.elements[1] = one*q.elements[1];
q.elements[2] = one*q.elements[2];
q.elements[3] = one*q.elements[3];
}
void EPdotdot_udot(ColMatrix& Audot, ColMatrix& Aqdot, ColMatrix& Aq, ColMatrix& Aqddot){
int num=Audot.GetNumRows();
if (3<num){
for (int i=4; i<=num; i++){
Aqddot.elements[i]=Audot.elements[i-1];
}
}
double AA;
AA=Aqdot.elements[0]*Aqdot.elements[0]+Aqdot.elements[1]*Aqdot.elements[1]+Aqdot.elements[2]*Aqdot.elements[2]+Aqdot.elements[3]*Aqdot.elements[3];
Aqddot.elements[0] = 0.5 *(Aq.elements[3]*Audot.elements[0] - Aq.elements[2]*Audot.elements[1] + Aq.elements[1]*Audot.elements[2]-2*Aq.elements[0]*AA);
Aqddot.elements[1] = 0.5 *(Aq.elements[2]*Audot.elements[0] + Aq.elements[3]*Audot.elements[1] - Aq.elements[0]*Audot.elements[2]-2*Aq.elements[1]*AA);
Aqddot.elements[2] = 0.5 *(-Aq.elements[1]*Audot.elements[0] + Aq.elements[0]*Audot.elements[1] + Aq.elements[3]*Audot.elements[2]-2*Aq.elements[2]*AA);
Aqddot.elements[3] = -0.5 *(Aq.elements[0]*Audot.elements[0] + Aq.elements[1]*Audot.elements[1] + Aq.elements[2]*Audot.elements[2]+2*Aq.elements[3]*AA);
}
void qdot_to_u(ColMatrix& q, ColMatrix& u, ColMatrix& qdot){
EP_Normalize(q);
int num=qdot.GetNumRows();
if (4<num){
for (int i=5; i<=num; i++){
u.elements[i-2]=qdot.elements[i-1];
}
}
u.elements[0]=2*(q.elements[3]*qdot.elements[0]+q.elements[2]*qdot.elements[1]-q.elements[1]*qdot.elements[2]-q.elements[0]*qdot.elements[3]);
u.elements[1]=2*(-q.elements[2]*qdot.elements[0]+q.elements[3]*qdot.elements[1]+q.elements[0]*qdot.elements[2]-q.elements[1]*qdot.elements[3]);
u.elements[2]=2*(q.elements[1]*qdot.elements[0]-q.elements[0]*qdot.elements[1]+q.elements[3]*qdot.elements[2]-q.elements[2]*qdot.elements[3]);
}
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