A Map Approximating the Phase Flow in the Problem of Attitude Motion of Celestial Bodies

We consider the motion of an axisymmetric celestial body with respect to the center of mass under gravitational torque. 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 symmetry axis is zero, then “planar” motions are possible, i.e., motions in which the symmetry axis moves in the plane of the orbit. To analyze the properties of the motions of the body that are close to long-periodic planar motions, we construct a map by perturbation theory methods that approximates the map generated by the phase flow of the system. Using this map, we establish previously unknown properties of the attitude motion of celestial bodies.