Satellite in elliptical orbit: on numerical detection of periodic movements and analysis of their stability

The equations of plane oscillations of a satellite in an elliptical orbit are considered. For the numerical detection of periodic solutions, a combination of the Poincaré section method and the previously proposed approach based on an analogue of the principle of contraction mappings is used. A number of classes of periodic solutions are numerically identified, and necessary conditions for their stability are studied. These motions are given special attention, since, in the general case, they are difficult to study analytically.