Map approximating phase flow in the problem of attitude motion of celestial bodies

The attitude motion of an axisymmetric celestial body under the influence of a gravitational torque is studied. The center of mass of the body moves in a circular orbit in a central gravitational field. If the projection of the angular momentum vector of the body onto its axis of symmetry is zero, then so-called "planar" motions are possible. In planar motions the axis of symmetry moves in the orbital plane and, therefore, the angular velocity vector of the body is perpendicular to this plane. To analyze the properties of the motions, which are close to planar ones, perturbation theory is applied. A map is constructed that approximates the map generated by the phase flow of the system. Using constucted map, we were able to establish some previously unknown properties of the attitude motion of celestial bodies.