Invariant sets and polhodes in the rigid body problem

Abstract

In this work we will describe the sets in the rigid body phase space where the energy and angular momentum are constant, and it will turn out that in nontrivial cases they will simply take the form of cartesian products of the polhodes byS1. These sets are important for the global study of said geodesic mechanical system for being invariant under Euler's equations (energy and momentum are constant along their solutions).