Partial reductions of Hamiltonian flows and Hess-Appel'rot systems on SO(n)

Abstract

We study reductions of the Hamiltonian flows restricted to their invariant submanifolds. As examples, we consider partial Lagrange-Routh reductions of the natural mechanical systems such as geodesic flows on compact Lie groups and n-dimensional variants of the classical Hess-Appel'rot case of a heavy rigid body motion about a fixed point.