The fast spinning motion of a rigid body in the presence of a gyrostatic momentum l3

In this paper, the rotational motion of a rigid body about a fixed point in the Newtonian force field [1] with a gyrostatic momentum l(3) about the z-axis is considered. The equations of motion and their first integrals are obtained and reduced to a quasi-linear autonomous system with two degrees of freedom with one First integral. Poincare's small parameter method [2] 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 [3] to describe the orientation of the body at any instant of time.