The Separatrix Algorithmic Map: Application to The Spin-Orbit Motion

Abstract

AbstractThe planar rotational motion of a non-symmetric satellite in an elliptic orbit is considered. A two-dimensional map is constructed, describing the motion 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 that 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 (Wisdom, 1987)) of the phase space of spin-orbit coupling for non-symmetric natural satellites. Moreover, it provides a straightforward analytical description of the phase space: analysis of properties of the map allows one to precalculate, by means of compact analytical relations, the locations of resonances and chaos borders, the emergence of marginal resonances, and even to describe bifurcations of the synchronous resonance’s center, though far from the separatrix.