STABILITY OF STEADY ROTATIONS OF A BODY FILLED WITH A LIQUID AND SUSPENDED BY A STRING

摘要

A model of motion of a heavy dynamically symmetric body with an ellipsoidal axisymmetric cavity filled entirely with a perfect incompressible liquid is considered. The liquid is in uniform vortex motion. The body is suspended by a rigid inextensible string. The steady rotations of the body and of the liquid in the cavity about their common axis of symmetry are analyzed. The following results are obtained: 1) if the liquid slowly rotates inside the cavity, then the steady motions are stable and do not depend on the angular velocity of the body; 2) if the rotation of the liquid in the cavity is fast, then a certain degree of oblateness of the cavity along the axis of symmetry is a sufficient condition of stability; 3) several sufficient conditions of stability are obtained in the form of inequalities imposed on the problem's parameters for the case when the body and the liquid rotate as a single body.