[[Imported from SVN: r7868]]

[[Imported from SVN: r7867]]

[[Imported from SVN: r7866]]

[[Imported from SVN: r7865]]

framework wants a global function space basis.

So far the P1 basis is hardwired for simplicity.

[[Imported from SVN: r7863]]

[[Imported from SVN: r7860]]

[[Imported from SVN: r7856]]

[[Imported from SVN: r7848]]

[[Imported from SVN: r7847]]

[[Imported from SVN: r7843]]

[[Imported from SVN: r7842]]

[[Imported from SVN: r7841]]

[[Imported from SVN: r7840]]

Computation of analytical energy gradients doesn't work, yet.

[[Imported from SVN: r7839]]

[[Imported from SVN: r7838]]

[[Imported from SVN: r7837]]

We need the extra flexibility for higher-order functions.
Run-time loss is around 1% -- that's okay.

[[Imported from SVN: r7836]]

[[Imported from SVN: r7620]]

[[Imported from SVN: r7617]]

[[Imported from SVN: r7616]]

[[Imported from SVN: r7614]]

[[Imported from SVN: r7613]]

[[Imported from SVN: r7611]]

[[Imported from SVN: r7576]]

notably the almost-equivalent UnitVector<4>: A vector with three entries
is interpreted by the UnitVector<4> class as a tangent vector given in
the basis returned by orthonormalFrame.  That is correct as it works
for all kinds of manifolds.  On the other hand, the Rotation<3> class
interprets as a 3x3 skew matrix (a tangent vector at the identity in
the matrix representation) even though the implementation used quaternion
coordinates.

To trick around this the use of exp methods with FieldVector<3> is avoided
by this patch.  A real fix would involve introducing a SkewMatrix class
and using that in Rotation<3>.

[[Imported from SVN: r7575]]

[[Imported from SVN: r7574]]

[[Imported from SVN: r7573]]

[[Imported from SVN: r7572]]

[[Imported from SVN: r7571]]

[[Imported from SVN: r7570]]

[[Imported from SVN: r7569]]

[[Imported from SVN: r7568]]

[[Imported from SVN: r7567]]

[[Imported from SVN: r7566]]

coordinates into a separate method, and fix an index bug on the way.
Now this derivative passes an fd check.

[[Imported from SVN: r7565]]

[[Imported from SVN: r7564]]

[[Imported from SVN: r7563]]

move method getFirstDerivativesOfDirectors into the rotation class.  It does not make sense for general quaternions

[[Imported from SVN: r7562]]

[[Imported from SVN: r7561]]

[[Imported from SVN: r7560]]