Rot.cc

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/* $Header: /var/cvs/mbdyn/mbdyn/mbdyn-1.0/libraries/libmbmath/Rot.cc,v 1.32 2017/01/12 14:43:53 masarati Exp $ */
/* 
 * HmFe (C) is a FEM analysis code. 
 *
 * Copyright (C) 1996-2017
 *
 * Marco Morandini  <morandini@aero.polimi.it>
 * Teodoro Merlini  <merlini@aero.polimi.it>
 *
 * Dipartimento di Ingegneria Aerospaziale - Politecnico di Milano
 * via La Masa, 34 - 20156 Milano, Italy
 * http://www.aero.polimi.it
 *
 * Changing this copyright notice is forbidden.
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.
 *
 */
/*
 * MBDyn (C) is a multibody analysis code. 
 * http://www.mbdyn.org
 *
 * Copyright (C) 1996-2017
 *
 * This code is a partial merge of HmFe and MBDyn.
 *
 * Pierangelo Masarati  <masarati@aero.polimi.it>
 * Paolo Mantegazza     <mantegazza@aero.polimi.it>
 *
 * Dipartimento di Ingegneria Aerospaziale - Politecnico di Milano
 * via La Masa, 34 - 20156 Milano, Italy
 * http://www.aero.polimi.it
 *
 * Changing this copyright notice is forbidden.
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation (version 2 of the License).
 * 
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA
 */

#include "mbconfig.h"           /* This goes first in every *.c,*.cc file */

#include <iostream>
#include "mathtyp.h"
#include "matvecexp.h"
#include "RotCoeff.hh"
#include "Rot.hh"

using namespace RotCoeff;

Mat3x3 RotManip::Rot(const Vec3 & phi) {
        doublereal coeff[COEFF_B];

        CoeffB(phi,phi,coeff);

        Mat3x3 Phi(1., phi*coeff[0]);           /* I + c[0] * phi x */
        Phi += Mat3x3(MatCrossCross, phi, phi*coeff[1]);        /* += c[1] * phi x phi x */

        return Phi;
}


Mat3x3 RotManip::DRot(const Vec3 & phi) {
        doublereal coeff[COEFF_C];

        CoeffC(phi,phi,coeff);

        Mat3x3 Ga(1., phi*coeff[1]);            /* I + c[0] * phi x */
        Ga += Mat3x3(MatCrossCross, phi, phi*coeff[2]); /* += c[1] * phi x phi x */

        return Ga;
}


void RotManip::RotAndDRot(const Vec3 & phi, Mat3x3 & Phi, Mat3x3 & Ga) {
        doublereal coeff[COEFF_C];

        CoeffC(phi,phi,coeff);

        Phi = Mat3x3(1., phi*coeff[0]);
        Phi += Mat3x3(MatCrossCross, phi, phi*coeff[1]);

        Ga = Mat3x3(1., phi*coeff[1]);
        Ga += Mat3x3(MatCrossCross, phi, phi*coeff[2]);

        return;
}

Mat3x3 RotManip::DRot_IT(const Vec3 & phi) {
        doublereal coeff[COEFF_D], coeffs[COEFF_C_STAR];
        
        CoeffCStar(phi,phi,coeff,coeffs);

        Mat3x3 GaIT(1., phi*.5);
        GaIT += Mat3x3(MatCrossCross, phi, phi*coeffs[0]);

        return GaIT;
}

Mat3x3 RotManip::DRot_I(const Vec3 & phi) {
        doublereal coeff[COEFF_D], coeffs[COEFF_C_STAR];
        
        CoeffCStar(phi,phi,coeff,coeffs);

        Mat3x3 GaI(1., phi*(-.5));
        GaI += Mat3x3(MatCrossCross, phi, phi*coeffs[0]);

        return GaI;
}

void RotManip::RotAndDRot_IT(const Vec3 & phi, Mat3x3 & PhiIT, Mat3x3 & GaIT) {
        doublereal coeff[COEFF_D], coeffs[COEFF_C_STAR];

        CoeffCStar(phi,phi,coeff,coeffs);

        PhiIT = Mat3x3(1., phi*coeff[0]);
        PhiIT += Mat3x3(MatCrossCross, phi, phi*coeff[1]);

        GaIT = Mat3x3(1., phi*.5);
        GaIT += Mat3x3(MatCrossCross, phi, phi*coeffs[0]);

        return;
}

Vec3 RotManip::VecRot(const Mat3x3 & Phi) {
        doublereal a, cosphi, sinphi;
        Vec3 unit;

        // Modified from Appendix 2.4 of
        //
        // author = {Marco Borri and Lorenzo Trainelli and Carlo L. Bottasso},
        // title = {On Representations and Parameterizations of Motion},
        // journal = {Multibody System Dynamics},
        // volume = {4},
        // pages = {129--193},
        // year = {2000}

        cosphi = (Phi.Trace() - 1.)/2.;
        if (cosphi > 0.) {
                unit = Phi.Ax();
                sinphi = unit.Norm();
                doublereal phi = atan2(sinphi, cosphi);
                CoeffA(phi, Vec3(phi, 0., 0.), &a);
                unit /= a;
        } else {
                // -1 <= cosphi <= 0
                Mat3x3 eet(Phi.Symm());
                eet(1, 1) -= cosphi;
                eet(2, 2) -= cosphi;
                eet(3, 3) -= cosphi;
                // largest (abs) component of unit vector phi/|phi|
                Int maxcol = 1;
                if (eet(2, 2) > eet(1, 1)) {
                        maxcol = 2;
                }
                if (eet(3, 3) > eet(maxcol, maxcol)) {
                        maxcol = 3;
                }
                unit = (eet.GetVec(maxcol)/sqrt(eet(maxcol, maxcol)*(1. - cosphi)));
                // sinphi = -(Mat3x3(unit)*Phi).Trace()/2.;
                sinphi = -(unit.Cross(Phi)).Trace()/2.;
                unit *= atan2(sinphi, cosphi);
        }
        return unit;
}

Mat3x3 RotManip::Elle
        (const Vec3 & phi,
        const Vec3 & a) {
    doublereal coeff[COEFF_E];
    CoeffE(phi,phi,coeff);
    
    Mat3x3 L(MatCross, a*(-coeff[1]));
    L -= Mat3x3(MatCrossCross, phi, a*coeff[2]);
    L -= Mat3x3(MatCross, phi.Cross(a*coeff[2]));
    L += (phi.Cross(a)).Tens(phi*coeff[3]);
    L += (Mat3x3(MatCrossCross, phi, phi)*a).Tens(phi*coeff[4]);

    return L;
}

MatExp RoTrManip::Elle
        (const VecExp & phi,
        const VecExp & a) {
    ScalExp coeff[COEFF_E];
    CoeffE(phi,phi.GetVec(),coeff);
    
    MatExp L(a*(-coeff[1]));
    L -= MatExp(phi,a*coeff[2]);
    L -= MatExp(phi.Cross(a*coeff[2]));
    L += (phi.Cross(a)).Tens(phi*coeff[3]);
    L += (MatExp(phi,phi)*a).Tens(phi*coeff[4]);

    return L;
}

MatExp RoTrManip::RoTr(const VecExp & phi) {
        ScalExp coeff[COEFF_B];

        CoeffB(phi,phi.GetVec(),coeff);

        MatExp Phi(1., phi*coeff[0]);   /* I + c[0] * phi x */
        Phi += MatExp(phi, phi*coeff[1]);       /* += c[1] * phi x phi x */

        return Phi;
}

MatExp RoTrManip::DRoTr(const VecExp & phi) {
        ScalExp coeff[COEFF_C];

        CoeffC(phi,phi.GetVec(),coeff);

        MatExp Ga(1., phi*coeff[1]);            /* I + c[0] * phi x */
        Ga += MatExp(phi, phi*coeff[2]);        /* += c[1] * phi x phi x */

        return Ga;
}

void RoTrManip::RoTrAndDRoTr(const VecExp & phi, MatExp & Phi, MatExp & Ga) {
        ScalExp coeff[COEFF_C];

        CoeffC(phi,phi.GetVec(),coeff);

        Phi = MatExp(1., phi*coeff[0]);
        Phi += MatExp(phi, phi*coeff[1]);

        Ga = MatExp(1., phi*coeff[1]);
        Ga += MatExp(phi, phi*coeff[2]);

        return;
}

MatExp RoTrManip::DRoTr_It(const VecExp & phi) {
        ScalExp coeff[COEFF_D], coeffs[COEFF_C_STAR];
        
        CoeffCStar(phi,phi.GetVec(),coeff,coeffs);

        MatExp GaIT(1., phi*.5);
        GaIT += MatExp(phi, phi*coeffs[0]);

        return GaIT;
}

MatExp RoTrManip::DRoTr_I(const VecExp & phi) {
        ScalExp coeff[COEFF_D], coeffs[COEFF_C_STAR];
        
        CoeffCStar(phi,phi.GetVec(),coeff,coeffs);

        MatExp GaIT(1., phi*-.5);
        GaIT += MatExp(phi, phi*coeffs[0]);

        return GaIT;
}

void RoTrManip::RoTrAndDRoTr_It(const VecExp & phi, 
                                MatExp & PhiIT,
                                MatExp & GaIT) {
        ScalExp coeff[COEFF_D], coeffs[COEFF_C_STAR];

        CoeffCStar(phi,phi.GetVec(),coeff,coeffs);

        PhiIT = MatExp(1., phi*coeff[0]);
        PhiIT += MatExp(phi, phi*coeff[1]);

        GaIT = MatExp(1., phi*.5);
        GaIT += MatExp(phi, phi*coeffs[0]);

        return;
}

VecExp RoTrManip::Helix(const MatExp & H)  {
        Vec3 phi(RotManip::VecRot(H.GetVec()));
        return VecExp(phi,
                        RotManip::DRot_IT(phi).Transpose()*(
                                (H.GetMom()*(H.GetVec().Transpose())).Ax())
                        );
}

namespace ER_Rot {
Param_Manip Param;
MatR_Manip MatR;
MatG_Manip MatG;
MatGm1_Manip MatGm1;
} // end of namespace ER_Rot