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

The subject of the study is the problem of precession of a gyrostat with a fixed point in three homogeneous force fields. The class of precessional movements under consideration is characterized by the properties of constancy of the nutation angle and commensurability of the precession rates and the gyrostat’s own rotation. The equations of motion of the gyrostat are reduced to three second-order differential equations with respect to the precession rates and the proper rotation of the gyrostat. Integration of these equations was carried out in the case of precessional-isoconic movements (the speeds of precession and proper rotation are equal) and in one case the resonant values of the speeds of precession and proper rotation (the precession speed is twice the speed of proper rotation – resonance 2 : 1). It is proven that the solutions obtained in the article are characterized by elementary functions of time.