Celestial Mechanics and Dynamical Astronomy

, Volume 59, Issue 2, pp 129–148 | Cite as

Surfaces of section in the Miranda-Umbriel 3:1 inclination problem

  • Michèle Moons
  • Jacques Henrard
Article

Abstract

The recent numerical simulations of Tittemore and Wisdom (1988, 1989, 1990) and Dermottet 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 landscape 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 3:1 inclination resonance between Miranda and Umbriel is analysed.

Key words

orbit-orbit resonance chaotic layers secondary resonances perturbation theory 

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Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Michèle Moons
    • 1
  • Jacques Henrard
    • 1
  1. 1.Département de Mathématique FUNDP 8NamurBelgique

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