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Chaotic Layers in Resonance Problems

Published online by Cambridge University Press:  07 August 2017

Jacques Henrard ,
Michèle Moons  and
Alessandro Morbidelli
Jacques Henrard
Affiliation:
Département de mathématique FUNDP 8, Rempart de la Vierge, B-5000 Namur, Belgique
Michèle Moons
Affiliation:
Département de mathématique FUNDP 8, Rempart de la Vierge, B-5000 Namur, Belgique
Alessandro Morbidelli
Affiliation:
Département de mathématique FUNDP 8, Rempart de la Vierge, B-5000 Namur, Belgique

Abstract

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The recent numerical simulations of Tittemore and Wisdom (1988,1989,1990) and Dermott et al. (1988), Malhotra and Dermott (1990) concerning the tidal evolution through resonances of some pairs of Uranian satellites have revealed interesting dynamical phenomena related to the interactions between close-by resonances. These interactions produce chaotic layers and strong secondary resonances. The slow evolution of the satellite orbits in this dynamical lanscape is responsible for temporary capture into resonance, enhancement of eccentricity or inclination and subsequent escape from resonance. The present contribution aims at developing analytical tools for predicting the location and size of chaotic layers and secondary resonances. The problem of the 1:3 inclination resonance between Miranda and Umbriel is analysed.

Keywords

orbit-orbit resonancechaotic layerssecondary resonanceperturbation theory
Type
Part IV - Planetary Satellites
Information
Symposium - International Astronomical Union , Volume 152: Chaos, Resonance and Collective Dynamical Phenomena in the Solar System , 1992 , pp. 189 - 208
Copyright
Copyright © Kluwer 1992 

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