On the dynamical symmetry points and the orientations of the principal axes of inertia of a rigid body

For an arbitrary rigid body, all dynamical symmetry points are found, and the directions of the axes of dynamical symmetry are determined for these points. We obtain conditions on the principal central moments of inertia under which the Lagrange and Kovalevskaya cases can be realized for the rigid body. We also analyze the set of orientations of the bases formed by the principal axes of inertia for various points of the rigid body.