On the Motion of a Rigid Body in the Presence of a Gyrostatic Momentum

Abstract

In this paper, the rotational motion ofa rigid body about a fixed point in the Newtonian force field with a gyrostatic momentum l₃ about z- axis is considered. The equations of motion and their first integrals are obtained and have been reduced to a quasilinear autonomous system of two degrees offreedom with one first integral. Poincaré’s small parameter method (Malkin, 1959) is applied to investigate the analytical periodic solutions of the equations of motion of the body with one point fixed. rapidly spinning about one of the principal axes of the ellipsoid of inertia. A geometric interpretation of motion is given by using Euler’s angles (Ismail, 1997a) to describe the orientation ofthe body at any instant of time.