LIMITING CASE FOR THE MOTION OF A RIGID-BODY ABOUT A FIXED-POINT IN THE NEWTONIAN FORCE-FIELD

In the present paper the motion of a rigid body about a fixed point in a central Newtonian force field is considered. It is assumed, that th e center of mass of the body is not necessarily coinciding with the fi xed point and its ellipsoid of inertial is arbitrary. It is taken into consideration, that the body has a sufficiently large initial angular velocity (r(0)) about the minor or the major principal axis of the el lipsoid of inertial and that the parameter (1/r(0)) is small. The equa tions of motion and their available first integrals are reduced to a q uasilinear autonomous system of two degrees of freedom with one first integral. The method of Poincare [1] and its modifications [2] and [3] are applied to construct periodic solutions for the autonomous system obtained in the case when the two frequencies of the generating syste m are distinct but commensurable (except omega = 1/2, 1, 2). We restri ct ourselves to determine such solutions and the expressions of the Eu lerian angles for the limiting case gamma(0)('') approximate to 0. At the end, a fourth order Runge-Kutta method [4] is applied to investiga te the numerical solutions of the autonomous system. Then, the graphic al representations for both the numerical and the analytical solutions are obtained. A comparison between them shows that the results coinci de and the deviations are very small.