A MOTION OF A FAST SPINNING RIGID BODY ABOUT A FIXED POINT IN A SINGULAR CASE (Annual of Sofia University St. Kliment Ohridski. Faculty of Mathematics and Informatics, 1998)
In this paper the problem of motion of a rigid body about a fixed point under the action of a Newtonian force field is studied for a singular value of the natural frequency ($ω=1/3$). This singularity deals with different bodies being classified according to the moments of inertia. Using Poincaré's small parameter method, the periodic solutions - with non-zero basic amplitudes - of the quasi-linear autonomous system are obtained in the form of power series expansions, up to the third approximation, containing assumed small parameter. Also, the quasi-linear autonomous system is integrated numerically using any of the numerical integration methods, such as the fourth order Runge-Kutta method. At the end, a comparison between the analytical and the numerical solutions is given aiming to get a small deviation between them.