Nonregular precession of a rigid body in three uniform fields

Abstract

This article presents a solution to the problem of the conditions of nonregular precession of a rigid body in three homogeneous fields, in which the ratio of precession and proper rotation velocities is constant. It is shown that the precession of a dynamically symmetric body is possible at a precession velocity equal to, twice as large as, or twice as small as the proper rotation velocity. For each of the cases, the set of admissible positions of the centres of the forces and the relation between the body moments of inertia and constant nutation angle are given.