spatialTransform: Compact representation of the Plücker spatial transformation tensor
in terms of the rotation tensor \c E and translation vector \c r .
See Chapter 2 and Appendix A in reference:
Featherstone, R. (2008).
Rigid body dynamics algorithms.
Springer.
This work is sponsored by Carnegie Wave Energy Ltd
Henry G. Weller
CFD Direct
This commit is contained in:
Henry Weller
@ -0,0 +1,200 @@
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/*---------------------------------------------------------------------------*\
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration |
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\\ / A nd | Copyright (C) 2016 OpenFOAM Foundation
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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This file is part of OpenFOAM.
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OpenFOAM is free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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for more details.
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You should have received a copy of the GNU General Public License
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along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
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Class
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Foam::spatialTransform
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Description
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Compact representation of the Plücker spatial transformation tensor
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in terms of the rotation tensor \c E and translation vector \c r .
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See Chapter 2 and Appendix A in reference:
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\verbatim
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Featherstone, R. (2008).
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Rigid body dynamics algorithms.
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Springer.
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\endverbatim
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SourceFiles
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spatialTransformI.H
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\*---------------------------------------------------------------------------*/
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#ifndef spatialTransform_H
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#define spatialTransform_H
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#include "tensor.H"
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#include "spatialVector.H"
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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namespace Foam
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{
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// Forward declaration of classes
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class Istream;
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class Ostream;
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// Forward declaration of friend functions and operators
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class spatialTransform;
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Istream& operator>>(Istream&, spatialTransform&);
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Ostream& operator<<(Ostream&, const spatialTransform&);
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/*---------------------------------------------------------------------------*\
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Class spatialTransform Declaration
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\*---------------------------------------------------------------------------*/
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class spatialTransform
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{
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// Private data
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//- Rotation tensor
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tensor E_;
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//- Translation vector
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vector r_;
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// Private member functions
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//- Return E . *r
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inline tensor Erx() const;
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public:
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//- Wrapper-class to provide transpose functions and operators
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class transpose
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{
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const spatialTransform& X_;
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public:
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//- Construct from a spatialTransform
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inline transpose(const spatialTransform& X);
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//- Return the transpose transformation tensor ^A{X^*}_B
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// X^T
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inline operator spatialTensor() const;
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//- Transpose transform dual f: ^A{X^*}_B & f
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// X^T . f = (E^T . fl + r ^ E^T . fw, E^T . fl)
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inline spatialVector operator&(const spatialVector& f) const;
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};
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//- Wrapper-class to provide dual functions and operators
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class dual
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{
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const spatialTransform& X_;
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public:
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//- Construct from a spatialTransform
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inline dual(const spatialTransform& X);
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//- Return dual transformation tensor ^B{X^*}_A
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inline operator spatialTensor() const;
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//- Transform dual f: ^B{X^*}_A & f
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// X^* . f = (E . fw - r ^ fl, E . fl)
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inline spatialVector operator&(const spatialVector& f) const;
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};
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// Constructors
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//- Construct null
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inline spatialTransform();
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//- Construct from components
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inline spatialTransform(const tensor& E, const vector& r);
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//- Construct from Istream
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inline spatialTransform(Istream&);
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// Member Functions
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//- Return the rotation tensor
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inline const tensor& E() const;
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//- Return non-const access to the rotation tensor
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inline tensor& E();
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//- Return the translation vector
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inline const vector& r() const;
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//- Return non-const access to the translation vector
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inline vector& r();
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//- Return the transpose transformation tensor ^A{X^*}_B
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// X^T
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inline transpose T() const;
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//- Return the inverse transformation tensor: X^-1
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// X^-1 = (E^T, −E.r)
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inline spatialTransform inv() const;
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// Member Operators
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//- Return the dual transformation tensor ^B{X^*}_A
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inline dual operator*() const;
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//- Return transformation tensor ^BX_A
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// X
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inline operator spatialTensor() const;
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//- Inner-product multiply with a transformation tensor
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inline void operator&=(const spatialTransform& X);
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//- Return the inner-product of two transformation tensors
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inline spatialTransform operator&(const spatialTransform& X) const;
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//- Transform v: ^BX_A . v
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// X.v = (E . vw, E . (vl - r^vw))
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inline spatialVector operator&(const spatialVector& v) const;
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// IOstream Operators
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friend Istream& operator>>(Istream&, spatialTransform&);
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friend Ostream& operator<<(Ostream&, const spatialTransform&);
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};
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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} // End namespace Foam
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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#include "spatialTransformI.H"
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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#endif
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// ************************************************************************* //
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@ -0,0 +1,267 @@
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/*---------------------------------------------------------------------------*\
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========= |
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\\ / F ield | OpenFOAM: The Open Source CFD Toolbox
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\\ / O peration |
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\\ / A nd | Copyright (C) 2016 OpenFOAM Foundation
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\\/ M anipulation |
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-------------------------------------------------------------------------------
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License
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This file is part of OpenFOAM.
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OpenFOAM is free software: you can redistribute it and/or modify it
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under the terms of the GNU General Public License as published by
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the Free Software Foundation, either version 3 of the License, or
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(at your option) any later version.
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||||
OpenFOAM is distributed in the hope that it will be useful, but WITHOUT
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ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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||||
for more details.
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You should have received a copy of the GNU General Public License
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along with OpenFOAM. If not, see <http://www.gnu.org/licenses/>.
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\*---------------------------------------------------------------------------*/
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#include "transform.H"
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// * * * * * * * * * * * * * Private Member Functions * * * * * * * * * * * //
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Foam::tensor Foam::spatialTransform::Erx() const
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{
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return E_ & *r_;
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}
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// * * * * * * * * * * * * * * * * Constructors * * * * * * * * * * * * * * //
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inline Foam::spatialTransform::spatialTransform()
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:
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E_(tensor::I),
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r_(vector::zero)
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{}
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inline Foam::spatialTransform::spatialTransform
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(
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const tensor& E,
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const vector& r
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)
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:
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E_(E),
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r_(r)
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{}
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inline Foam::spatialTransform::spatialTransform(Istream& is)
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:
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E_(is),
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r_(is)
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{}
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inline Foam::spatialTransform::transpose::transpose(const spatialTransform& X)
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:
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X_(X)
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{}
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inline Foam::spatialTransform::dual::dual(const spatialTransform& X)
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:
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X_(X)
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{}
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// * * * * * * * * * * * * * * * Member Functions * * * * * * * * * * * * * //
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inline const Foam::tensor& Foam::spatialTransform::E() const
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{
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return E_;
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}
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inline Foam::tensor& Foam::spatialTransform::E()
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{
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return E_;
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}
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inline const Foam::vector& Foam::spatialTransform::r() const
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{
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return r_;
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}
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inline Foam::vector& Foam::spatialTransform::r()
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{
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return r_;
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}
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inline Foam::spatialTransform::transpose Foam::spatialTransform::T() const
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{
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return transpose(*this);
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}
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inline Foam::spatialTransform Foam::spatialTransform::inv() const
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{
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return spatialTransform(E_.T(), -(E_ & r_));
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}
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// * * * * * * * * * * * * * * * Member Operators * * * * * * * * * * * * * //
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inline Foam::spatialTransform::dual Foam::spatialTransform::operator*() const
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{
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return dual(*this);
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}
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inline Foam::spatialTransform::operator spatialTensor() const
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{
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return spatialTensor
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(
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E_, tensor::zero,
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-Erx(), E_
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);
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}
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inline void Foam::spatialTransform::operator&=(const spatialTransform& X)
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{
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E_ &= X.E_;
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r_ = X.r_ + (r_ & X.E_.T());
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}
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inline Foam::spatialTransform Foam::spatialTransform::operator&
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(
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const spatialTransform& X
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) const
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{
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return spatialTransform(E_ & X.E_, X.r_ + (r_ & X.E_));
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}
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inline Foam::spatialVector Foam::spatialTransform::operator&
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(
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const spatialVector& v
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) const
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{
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return spatialVector
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(
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E_ & v.angular(),
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E_ & (v.linear() - (r_ ^ v.angular()))
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);
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}
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inline Foam::spatialTransform::transpose::operator spatialTensor() const
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{
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return spatialTensor
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(
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X_.E().T(), -X_.Erx().T(),
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tensor::zero, X_.E().T()
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);
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}
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inline Foam::spatialVector Foam::spatialTransform::transpose::operator&
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(
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const spatialVector& f
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) const
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{
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vector ETfl(X_.E().T() & f.linear());
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return spatialVector
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(
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(X_.E().T() & f.angular()) + (X_.r() ^ ETfl),
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ETfl
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);
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}
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inline Foam::spatialTransform::dual::operator spatialTensor() const
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{
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return spatialTensor
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(
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X_.E(), -X_.Erx(),
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tensor::zero, X_.E()
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);
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}
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inline Foam::spatialVector Foam::spatialTransform::dual::operator&
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(
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const spatialVector& f
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) const
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{
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return spatialVector
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(
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X_.E() & (f.angular() - (X_.r() ^ f.linear())),
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X_.E() & f.linear()
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);
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}
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// * * * * * * * * * * * * * * IOstream Operators * * * * * * * * * * * * * //
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inline Foam::Istream& Foam::operator>>(Foam::Istream& is, spatialTransform& X)
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{
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is >> X.E() >> X.r();
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return is;
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}
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inline Foam::Ostream& Foam::operator<<
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(
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Foam::Ostream& os,
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const spatialTransform& X
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)
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{
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os << X.E() << token::SPACE << X.r() << endl;
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return os;
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}
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// * * * * * * * * * * * * * * * Global Functions * * * * * * * * * * * * * //
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namespace Foam
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{
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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//- Rotational spatial transformation tensor about the x-axis by omega radians
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inline spatialTransform Xrx(const scalar& omega)
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{
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return spatialTransform(Rx(omega), vector::zero);
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}
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//- Rotational spatial transformation tensor about the x-axis by omega radians
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inline spatialTransform Xry(const scalar& omega)
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{
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return spatialTransform(Ry(omega), vector::zero);
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}
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//- Rotational spatial transformation tensor about the z-axis by omega radians
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inline spatialTransform Xrz(const scalar& omega)
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{
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return spatialTransform(Rz(omega), vector::zero);
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}
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//- Rotational spatial transformation tensor about axis a by omega radians
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inline spatialTransform Xr(const vector& a, const scalar omega)
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{
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return spatialTransform(Ra(a, omega), vector::zero);
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}
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//- Translational spatial transformation tensor about axis a by omega radians
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inline spatialTransform Xt(const vector& r)
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{
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return spatialTransform(tensor::I, r);
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}
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// * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * //
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} // End namespace Foam
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// ************************************************************************* //
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Reference in New Issue
Block a user