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

Published online by Cambridge University Press:  12 April 2016

Ivan I. Shevchenko
Ivan I. Shevchenko*
Affiliation:
Pulkovo Observatory, Russian Academy of Sciences, Pulkovskoje ave. 6511, St.Petersburg 196140,Russia; E-mail: iis@gao.spb.ru

Abstract

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The 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.

Type
Analytical and Numerical Tools
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 259 - 268
Copyright
Copyright © Kluwer 1999

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