|XXVIII Workshop on Geometric Methods in Physics||28.06-04.07.2009|
Hess-Appel'rot Rigid Body Dynamics and Partial Symplectic Reductions
There are three famous integrable cases of a heavy rigid body motion: Euler, Lagrange and Kowalevskaya. Apart of these cases, there are various particular solutions. The celebrated is partially integrable Hess-Appel'rot case: under the Hess-Appel'rot conditions on inertia tensor, the Euler--Poisson equations have the invariant relation linear in momenta and the system restricted to the invariant manifold is integrable up to one quadrature.
We shall present an overview of the algebraic and geometrical aspects of the Hess--Appel'rot rigid body problem that lead to natural multidimensional generalizations of the system (joint work with Vladimir Dragovic and Borislav Gajic).