The separatrix algorithmic map: Application to the spin-orbit motion

The planar rotational motion of a non-symmetric satellite in an elliptic or bit is considered. A two-dimensional map is constructed, describing the mot ion in a vicinity of the separatrix of the synchronous spin-orbit resonance . This map is a generalization of Chirikov's separatrix map, in the sense t hat the asymmetry of perturbation is taken into account. Phase portraits of the generalized map perfectly reproduce well-known examples of surfaces of section (first computed by Wisdom et al. (Wisdom et al., 1984), Wisdom (Wi sdom, 1987)) of the phase space of spin-orbit coupling for non-symmetric na tural satellites. Moreover, it provides a straightforward analytical descri ption of the phase space: analysis of properties of the map allows one to p recalculate, by means of compact analytical relations, the locations of res onances and chaos borders, the emergence of marginal resonances, and even t o describe bifurcations of the synchronous resonance's center, though far f rom the separatrix.