Evolution of motion of a rigid body with a fixed point and an ellipsoidal cavity filled with a viscous fluid

The inertial motion of a system consisting of a solid with a fixed point and a viscous incompressible liquid filling a spherical or ellipsoidal cavity inside the body is considered. The principal moments of inertia of the system about a fixed point are approximately equal to the principal moments of inertia of an axisymmetric body. The Reynolds number being inversely proportional to the viscosity of the liquid is assumed to be small. For the description of motion, the generalized canonical variables of Ђndoyer, the motion separation method, and the averaging method are used. It is shown that the motion of the system tends to the steady rotation about the axis of the greatest moment of inertia directed along the constant angular momentum vector of the system.