Steady motions of nonhomogeneous ellipsoid on horizontal plane

The dynamics of a heavy nonhomogeneous ellipsoid of rotation on a horizontal fixed plane with friction is analysed. It is assumed that the mass centre of the spheroid coincides with its geometric center and that the geometric axis of symmetry is the axis of dynamic symmetry. The frictional force is proportional to the velocity of the point of contact with the plane; the frictional moment is equal to zero. The steady motions of the ellipsoid are investigated. The conditions of stability are obtained. The results are compared with the corresponding results in the case of an absolutely smooth and absolutely rough surface. The unsteady motions of the spheroid are investigated numerically. The similar results for the special case of homogeneous ellipsoid have been given earlier [1].