On the motion of a heavy rigid body about a fixed point

Abstract

The paper considers the classical problem of the motion of a heavy rigid body about a fixed point. The Euler-Poisson equations are used for the presentation of that motion. Three first integrals of these equations are well known. To solve this problem completely one further first integral has to be found. The main purpose of the paper is to obtain a necessary and sufficient condition for some functionF(ω1,ω2,ω3,γ 1,γ 2,γ 3) to be a new first integral of Euler-Poisson equations.