The origin of chaotic behaviour in the Miranda-Umbriel 3 : 1 resonances

Details The origin of chaotic behaviour in the Miranda-Umbriel 3 : 1 resonances The origin of chaotic behaviour in the Miranda-Umbriel 3 : 1 resonances

Dec 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cemda..47..391h&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 47, Issue 4, pp.391-417

Astronomy and Astrophysics

Astronomy

1

Resonance, Chaotic Motion, Perturbation Theory, Tidal Evolution, Miranda

Scientific paper

We have investigated the pericentric resonances through which Miranda and Umbriel are believed to have passed when, due to tidal evolution, their orbital mean motions reached a 3 : 1 commensurability. Our investigation is based upon a perturbative treatment. The predictions of this theory are in good agreement with the results of numerical integrations concerning both the extend of the chaotic layers generated by the separatrices of the primary resonances and the location of the secondary resonances. The effect of tidal evolution is discussed on the bases of the adiatatic invariant theory and its extension to separatrix crossing. We recover qualitatively the mean features of the numerical experiments of Tittermore and Wisdom (1988 1989), Dermott et al (1988) and Malhotra and Dermott (1989).

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