The stability of the steady motions of a rigid body in a central field

The problem of the translational-rotational motion of a rigid body with a triaxial ellipsoid of inertia in a central gravitational field is considered. The body is modelled by a weightless sphere, at the ends of the three mutually perpendicular diameters of which there are point masses. It is shown that, unlike the cases when the approximate expression for the potential of the gravity forces is used, there are not only “trivial” steady motions of the body, for which the main central axes of inertia of the body coincide with the axes of the orbital system of coordinates, but also other classes of steady motions. In addition, the stability of these “trivial” steady motions is investigated, and the possibility of secular stability of the motions, unstable in the satellite approximation, is pointed out.