Regular Precession of an Asymmetrical Liquid-Filled Rigid Body in a Uniform Field

The Poincaré – Zhukovsky – Hough model describing the motion of a rigid body with an ellipsoidal cavity filled with an ideal vortex liquid is used. The possibility of regular precession in a uniform force field of a system not possessing axial symmetry is shown. For the case where the axis of proper rotation is one of the system principal inertia axes and the center of gravity lies on this axis, two conditions of precession are obtained. One of the conditions coincides with the condition of regular precession in the absence of external forces for the system without axial symmetry found earlier by the author. This condition imposes one constraint on the system configuration. The other condition relates the proper rotation and precession velocities to the mechanical parameters of the system. A record is given of the conditions in the form of relations between the inertia moments of the rigid shell and the semiaxes of the ellipsoidal cavity, as well as between the distance to the center of gravity and the nutation angle, the precession velocity and the proper rotation velocity. It is shown that in the case where the cavity differs little from the sphere, the conditions obtained differ from the Lagrange conditions for an axisymmetric rigid body with a fixed point in a uniform gravity field by small values of the second order.