To the theory of Resonant Rotation of the Mercury

The motion of a rigid body about its center of mass under action of gravitational moments of the central Newtonian force field is investigated. The orbit of the center of mass is proposed to be an elliptical one, the eccentricity of the orbit is equal to the one of the Mercury. The central ellipsoid of inertia of the body is arbitrary. The problem of existence of planar periodical rotations under resonance 3:2 of the Mercurian type is considered and their stability (in Liapunov) is investigated. In a case of planar perturbations the nonlinear problem of stability is solved. In a case of arbitrary perturbations of periodical rotations the stability in first (linear) approximation is investigated.