Precession Motions of a Gyrostat, Having a Fixed Point, in Three Homogeneous Force Fields

Abstract

The subject of investigation is the problem on precession motions of a gyrostat with a fixed point in three homogeneous force fields. The class of precessions under consideration is characterized by the constancy of the precession angle and by the commensurability of the precession and proper rotation velocities. Equations of motion of a gyrostat are reduced to a system of three second order differential equations with respect to velocities of precession and proper rotation. Integration of these equations is conducted in the case of precessionally isoconic motions (the precession velocity equals to the proper rotation velocity) and in the case of 2 : 1 resonance, when the precession velocity is two times more, than the proper rotation velocity. It is proved that the obtained solutions can be described by elementary functions of time.