98-470 Andreu M.A., Celletti A., Falcolini C.

Break-down of librational invariant surfaces (368K, LATeX2e) Jun 23, 98

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Abstract. A numerical investigation of the stability of invariant librational tori is presented. The method has been developed for a model describing the spin-orbit coupling in Celestial Mechanics. Periodic orbits approaching the librational torus are computed by means of a Newton's method. According to Greene's criterium, their stability is strictly related to the survival of invariant tori. We consider librational tori around the main spin-orbit resonances (1:1, 3:2). Their existence provides the stability of the resonances, due to confinement properties in the 3-dimensional phase space associated to our model. The results are consistent with the actual observations of the eccentricity and of the oblateness parameter. A different behaviour of the Moon and Mercury around the main resonances is evidentiated, providing interesting suggestions about the different probabilities of capture in a resonance.

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