Partial Reductions of Hamiltonian Flows and Hess-Appel'rot Systems on SO(n)

TL;DR

This paper investigates how Hamiltonian flows can be partially reduced on invariant submanifolds, with applications to geodesic flows on Lie groups and the Hess-Appel'rot rigid body system, providing new insights into their structure.

Contribution

It introduces partial reduction techniques for Hamiltonian flows and applies them to classical mechanical systems like geodesic flows and Hess-Appel'rot systems on SO(n).

Findings

Partial Lagrange-Routh reductions are developed for specific mechanical systems.

The study extends classical Hess-Appel'rot systems to n-dimensional cases.

New structural insights into Hamiltonian flows on Lie groups are provided.

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.