A second fundamental model for resonance

Abstract

We analyse a simple one degree of freedom Hamiltonian system depending upon a parameter\(H = - 3(\delta + 1)R + R^2 - 2\sqrt {2R} \cos r\). This model is much closer to resonance problems arising in Celestial Mechanics than the pendulum.

We deduce from it the conditions of capture into resonance or escape from resonance for systems drifting slowly. We apply this analysis to the Enceladus-Dione resonance.

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Supported by the ‘Fonds National de la Recherche Scientifique’.

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Henrard, J., Lemaitre, A. A second fundamental model for resonance. Celestial Mechanics 30, 197–218 (1983). https://doi.org/10.1007/BF01234306

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Keywords

  • Hamiltonian System
  • Celestial Mechanics
  • Fundamental Model
  • Resonance Problem
  • Freedom Hamiltonian System