The joint-space dynamics is solved on the master processor only and the
resulting joint-state distributed to the slave processors on which the
body-state is then updated.  This guarantees consistency of the body
position and orientation on all processors.

rigidBodyDynamics/bodies/sphere: Added support for the centre of mass being offset from the centre of rotation

Calculate the inertia from the lengths of the sides

Particularly useful for lists of dictionaries.

Patch provided by Bruno Santos
Resolves bug-report http://www.openfoam.org/mantisbt/view.php?id=2036

See also http://www.openfoam.org/mantisbt/view.php?id=2036

Patch contributed by Bruno Santos
Resolves bug-report http://www.openfoam.org/mantisbt/view.php?id=2052

rigidBodyMeshMotion: displacementMotionSolver for the mesh-motion of multiple articulated rigid-bodies

The motion of the bodies is integrated using the rigidBodyDynamics
library with joints, restraints and external forces.

The mesh-motion is interpolated using septernion averaging.

This development is sponsored by Carnegie Wave Energy Ltd.

Using method based on
http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20070017872.pdf
but simplified for the case where the quaternions are similar.

Patch contributed by Bruno Santos
Resolves bug-report http://www.openfoam.org/mantisbt/view.php?id=2055

Resolves bug-report http://www.openfoam.org/mantisbt/view.php?id=2053

Patch contributed by Bruno Santos

inline Foam::vector Foam::septernion::transformPoint(const vector& v) const
{
    return r().transform(v - t());
}

Now there is a 1:1 correspondence between septernion and
spatialTransform and a septernion constructor from spatialTransform
provided.

Additionally "septernion::transform" has been renamed
"septernion::transformPoint" to clarify that it transforms coordinate
points rather than displacements or other relative vectors.

Replaced with 'unitQuaterion()' virtual function to indicate if the
joint uses a unit quaternion to represent rotation.

rigidBodyDynamics: Simplify handling of quaternions by maintaining a unit quaternion in the joint state field 'q'

'w' is now obtained from 'v' using the relation w = sqrt(1 - |sqr(v)|)
and 'v' is stored in the joint state field 'q' and integrated in the
usual manner but corrected using quaternion transformations.

    //- Return the unit quaternion (versor) from the given vector
    //  (w = sqrt(1 - |sqr(v)|))
    static inline quaternion unit(const vector& v);

rigidBodyDynamics/rigidBodySolvers: Added run-time selectable solvers to integrate the rigid-body motion

Currently supported solvers: symplectic, Newmark, CrankNicolson

The symplectic solver should only be used if iteration over the forces
and body-motion is not required.  Newmark and CrankNicolson both require
iteration to provide 2nd-order behavior.

See applications/test/rigidBodyDynamics/spring for an example of the
application of the Newmark solver.

This development is sponsored by Carnegie Wave Energy Ltd.

“Error when reading ascii data. Possible mismatch of datasize with
declaration.”

Patch contributed by Karl Meredith, FMGlobal

This is a more convenient way of maintaining the state or multiple
states (for higher-order integration), storing, retrieving and passing
between processors.

Included for backward-compatibility with the 6-DoF solver but in the
future will be re-implemented as a joint rather than body restraint and
accumulated in tau (internal forces) rather than fx (external forces).