Stability of rigid body motion using the Energy-Casimir method

Holm, D. D., J. E. Marsden, T. Ratiu and A. Weinstein

Contemp. Math., 28, (1984), 15-23

Abstract:

The Energy-Casimir method, due to Newcomb, Arnold and others is illustrated by application to the motion of a free rigid body and the heavy top.
In the preceding paper of Weinstein, a general framework for calculating stability criteria is reviewed. In this note we illustrate the method in the concrete cases of a rigid body and heavy top. The classical stability results are obtained. The purpose of this note is to illustrate the basic ideas of the method with simple "hands-on" examples that should aid in the understanding of fluid and plasma examples in Holm's lecture that follows.