Introduction

Abstract

In classical mechanics a well defined concept of integrability exists which is related to the Hamiltonian description of mechanics. If the phase space of a mechanical system is 2n–dimensional, n integralsof motion in involution are suffcient for a complete description of the dynamics of the system. In this case the initial conditions specify the integrals of motion and thus the complete time evolution of the system. The task is to find such a system of integrals of motion. An importantexample for an integrable system in classical mechanics is the motion of a spinning top in the gravitational field of the Earth, the rotation of a rigid body about a fixed point (see e.g. [1], Chap.6and [2]). For a top where the orthogonal frame is attached to the body and where the axes coincide with the axes of inertia, the Hamilton function has the form