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Report About Long-time simulation for a rigid body 1.0
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These function implement Lie integrators to perform long time simulation of a rigid body in a static spring-magnetic potential field. This numerical test of symplecticity is detailed in:

Bou-Rabee, N., Ortolan, G., and Saccon, A. [2010].
A counterexample showing the semi-explicit Lie-Newmark algorithm is not variational. (preprint).

Results show the following:
(i) VLV algorithm exhibits no energy drift;
(ii) Lie-Newmark algorithm exhibits energy drift; and,
(iii) `explicit' Lie-Midpoint algorithm exhibits energy drift.

File details:
- basicrunem.m: launches the Lie methods;
- NMB.m: semi-explicit Lie-Newmark algorithm;
- LIEMIDEA.m: explicit Lie-Midpoint algorithm;
- VLV.m: Lie-Verlet algorithm;
- wedge.m: hat map.