RotManip Namespace Reference

Functions
Mat3x3	Rot (const Vec3 &phi)
Mat3x3	DRot (const Vec3 &phi)
void	RotAndDRot (const Vec3 &phi, Mat3x3 &Phi, Mat3x3 &Ga)
Mat3x3	DRot_IT (const Vec3 &phi)
Mat3x3	DRot_I (const Vec3 &phi)
void	RotAndDRot_IT (const Vec3 &phi, Mat3x3 &PhiIT, Mat3x3 &GaIT)
Vec3	VecRot (const Mat3x3 &Phi)
Mat3x3	Elle (const Vec3 &phi, const Vec3 &a)

Function Documentation

Mat3x3 RotManip::DRot

(

const Vec3 &

phi

)

Compute G matrix given Euler Rogriguez's parameters Phi G defined in such a way that dPhi * PhiT = G * dphi

Definition at line 74 of file Rot.cc.

References RotCoeff::COEFF_C, RotCoeff::CoeffC(), and MatCrossCross.

Referenced by Shell4EAS::AssJac(), Shell4EAS::ComputeIPCurvature(), Shell4EASANS::ComputeIPCurvature(), ER_Rot::MatG_Manip::Manipulate(), ER_Rot::MatG_Manip::operator<<(), and InvAngularConstitutiveLaw::Update().

                                      {
        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;
}

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Mat3x3 RotManip::DRot_I

(

const Vec3 &

phi

)

Compute the inverse of G matrix given Euler Rogriguez's parameters Phi

Definition at line 111 of file Rot.cc.

References RotCoeff::COEFF_C_STAR, RotCoeff::COEFF_D, RotCoeff::CoeffCStar(), and MatCrossCross.

Referenced by DriveHingeJoint::AfterPredict(), ElasticHingeJoint::AfterPredict(), ElasticJoint::AfterPredict(), ElasticHingeJointInv::AfterPredict(), ElasticJointInv::AfterPredict(), ViscoElasticJoint::AfterPredict(), ViscoElasticHingeJoint::AfterPredict(), ViscoElasticHingeJointInv::AfterPredict(), LoadIncNorm::AssJac(), ElasticAxialJoint::AssMat(), ElasticHingeJoint::AssMat(), Shell4EAS::ComputeIPCurvature(), Shell4EASANS::ComputeIPCurvature(), Shell4EAS::InterpolateOrientation(), Shell4EASANS::InterpolateOrientation(), main(), ER_Rot::MatGm1_Manip::Manipulate(), and ER_Rot::MatGm1_Manip::operator<<().

                                        {
        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;
}

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Mat3x3 RotManip::DRot_IT

(

const Vec3 &

phi

)

Compute the inverse transpose of G matrix given Euler Rogriguez's parameters Phi

Definition at line 100 of file Rot.cc.

References RotCoeff::COEFF_C_STAR, RotCoeff::COEFF_D, RotCoeff::CoeffCStar(), and MatCrossCross.

Referenced by Shell4EAS::AssJac(), and RoTrManip::Helix().

                                         {
        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;
}

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Mat3x3 RotManip::Elle	(	const Vec3 &	phi,
		const Vec3 &	a
	)

Compute, given Euler Rogriguez's parameters phi, L matrix such that dG * a = L(phi, a) * dphi

Definition at line 179 of file Rot.cc.

References a, RotCoeff::COEFF_E, RotCoeff::CoeffE(), Vec3::Cross(), MatCross, and MatCrossCross.

Referenced by Shell4EAS::AssJac(), Shell4EAS::ComputeIPCurvature(), and Shell4EASANS::ComputeIPCurvature().

                        {
    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;
}

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Mat3x3 RotManip::Rot

(

const Vec3 &

phi

)

Compute the rotation matrix Phi given Euler Rogriguez's parameters phi

Definition at line 62 of file Rot.cc.

References RotCoeff::COEFF_B, RotCoeff::CoeffB(), and MatCrossCross.

Referenced by ElasticHingeJointInv::AfterPredict(), ElasticDispJointInv::AfterPredict(), ElasticJointInv::AfterPredict(), ViscousHingeJointInv::AfterPredict(), ViscoElasticHingeJointInv::AfterPredict(), TotalEquation::AssRes(), TotalJoint::AssRes(), TotalPinJoint::AssRes(), GimbalRotationJoint::AssVec(), ElasticDispJointInv::AssVec(), ElasticHingeJointInv::AssVec(), ElasticJointInv::AssVec(), ViscousHingeJointInv::AssVec(), ViscoElasticHingeJointInv::AssVec(), DeformableHingeJoint::dGetPrivDataInv(), MBDynParser::GetMatR2vec(), TotalEquation::InitialAssRes(), TotalJoint::InitialAssRes(), TotalPinJoint::InitialAssRes(), Shell4EAS::InterpolateOrientation(), Shell4EASANS::InterpolateOrientation(), main(), ER_Rot::MatR_Manip::Manipulate(), ER_Rot::MatR_Manip::operator<<(), DeformableHingeJoint::OutputInv(), MBDynParser::Reference_int(), TotalPinJoint::SetValue(), DriveRigidBodyKinematics::Update(), InvAngularConstitutiveLaw::Update(), Shell4EAS::UpdateNodalAndAveragePosAndOrientation(), and Shell4EASANS::UpdateNodalAndAveragePosAndOrientation().

                                     {
        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;
}

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void RotManip::RotAndDRot	(	const Vec3 &	phi,
		Mat3x3 &	Phi,
		Mat3x3 &	Ga
	)

Compute rotation matrix Phi and Ga matrix given Euler Rogriguez's parameters Phi

Definition at line 86 of file Rot.cc.

References RotCoeff::COEFF_C, RotCoeff::CoeffC(), and MatCrossCross.

Referenced by Shell4EAS::InterpolateOrientation(), and Shell4EASANS::InterpolateOrientation().

                                                                     {
        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;
}

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void RotManip::RotAndDRot_IT	(	const Vec3 &	phi,
		Mat3x3 &	PhiIT,
		Mat3x3 &	GaIT
	)

Compute inverse transpose ot rotation matrix Phi and Ga matrix given Euler Rogriguez's parameters Phi

Definition at line 122 of file Rot.cc.

References RotCoeff::COEFF_C_STAR, RotCoeff::COEFF_D, RotCoeff::CoeffCStar(), and MatCrossCross.

                                                                            {
        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;
}

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Vec3 RotManip::VecRot

(

const Mat3x3 &

Phi

)

Compute Euler Rogriguez's parameters phi given rotation matrix Phi

Definition at line 136 of file Rot.cc.

References a, grad::atan2(), Mat3x3::Ax(), RotCoeff::CoeffA(), Vec3::Cross(), Vec3::Norm(), grad::sqrt(), Mat3x3::Symm(), and Mat3x3::Trace().

Referenced by AeroDynModule::AeroDynModule(), PlaneHingeJoint::AfterConvergence(), TotalJoint::AfterConvergence(), PlaneRotationJoint::AfterConvergence(), TotalPinJoint::AfterConvergence(), AxialRotationJoint::AfterConvergence(), PlanePinJoint::AfterConvergence(), DriveHingeJoint::AfterPredict(), ElasticAxialJoint::AfterPredict(), ElasticHingeJoint::AfterPredict(), ElasticJoint::AfterPredict(), ElasticHingeJointInv::AfterPredict(), ElasticDispJointInv::AfterPredict(), ElasticJointInv::AfterPredict(), ViscoElasticAxialJoint::AfterPredict(), ViscousHingeJointInv::AfterPredict(), ViscoElasticJoint::AfterPredict(), ViscoElasticHingeJoint::AfterPredict(), ViscoElasticHingeJointInv::AfterPredict(), angle(), anglerel(), DataManager::AssConstrRes(), LoadIncNorm::AssRes(), AerodynamicModal::AssRes(), TotalEquation::AssRes(), TotalJoint::AssRes(), Modal::AssRes(), ClampJoint::AssRes(), TotalPinJoint::AssRes(), GimbalRotationJoint::AssVec(), DriveHingeJoint::AssVec(), ElasticAxialJoint::AssVec(), ElasticHingeJoint::AssVec(), ElasticJoint::AssVec(), ElasticDispJointInv::AssVec(), ElasticHingeJointInv::AssVec(), ElasticJointInv::AssVec(), ViscoElasticAxialJoint::AssVec(), ViscousHingeJointInv::AssVec(), ViscoElasticJoint::AssVec(), ViscoElasticHingeJoint::AssVec(), ViscoElasticHingeJointInv::AssVec(), ViscousBody::dGetPrivData(), DeformableAxialJoint::dGetPrivData(), DeformableJoint::dGetPrivData(), DeformableHingeJoint::dGetPrivData(), PlaneHingeJoint::dGetPrivData(), TotalJoint::dGetPrivData(), PlaneRotationJoint::dGetPrivData(), Beam2::dGetPrivData(), Beam::dGetPrivData(), TotalPinJoint::dGetPrivData(), AxialRotationJoint::dGetPrivData(), PlanePinJoint::dGetPrivData(), StructNode::dGetPrivData(), DeformableHingeJoint::dGetPrivDataInv(), Eu2PhiWrap::Get(), getbladeparams(), getelemparams(), RoTrManip::Helix(), DriveHingeJoint::InitialAssRes(), TotalEquation::InitialAssRes(), TotalJoint::InitialAssRes(), TotalPinJoint::InitialAssRes(), ViscoElasticAxialJoint::InitialAssRes(), ViscoElasticHingeJoint::InitialAssRes(), main(), ER_Rot::Param_Manip::Manipulate(), MatManip_test(), ER_Rot::Param_Manip::operator<<(), ReferenceFrame::Output(), GimbalRotationJoint::Output(), SphericalHingeJoint::Output(), DeformableAxialJoint::Output(), DeformableHingeJoint::Output(), DeformableJoint::Output(), Inertia::Output(), StructExtForce::Output(), PlaneHingeJoint::Output(), UniversalRotationJoint::Output(), TotalEquation::Output(), TotalJoint::Output(), Beam2::Output(), PlaneRotationJoint::Output(), Beam::Output(), TotalReaction::Output(), TotalPinJoint::Output(), AxialRotationJoint::Output(), StructNode::Output(), Inertia::Output_int(), Aerodynamic2DElem< iNN >::Output_int(), DataManager::OutputEigGeometry(), DeformableHingeJoint::OutputInv(), ReadStructExtForce(), ReadStructNode(), StructExtForce::SendToFileDes(), StructMappingExtForce::SendToFileDes(), StructMembraneMappingExtForce::SendToFileDes(), StructExtForce::SendToStream(), StructMappingExtForce::SendToStream(), StructMembraneMappingExtForce::SendToStream(), PlaneHingeJoint::SetValue(), PlaneRotationJoint::SetValue(), PlanePinJoint::SetValue(), TotalJoint::TotalJoint(), TotalPinJoint::TotalPinJoint(), Shell4EAS::UpdateNodalAndAveragePosAndOrientation(), and Shell4EASANS::UpdateNodalAndAveragePosAndOrientation().

                                        {
        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;
}

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