- 98-470 Andreu M.A., Celletti A., Falcolini C.
- Break-down of librational invariant surfaces
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.