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A Comparison of the Mean-Value and Initial-Value Solutions of the Ideal Resonance Problem with an Application in Rigid-Body Mechanics

Published online by Cambridge University Press:  14 August 2015

A. H. Jupp
A. H. Jupp*
Affiliation:
The University of Liverpool, U.K.

Abstract

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A solution of the ideal resonance problem has already been exhibited (Jupp, 1972) explicitly in terms of the ‘mean’ elements; to second order in the small parameter in the case of libration, and to first order in the case of deep circulation. Both representations possess a singularity when the ‘mean’ modulus of the Jacobi elliptic functions is unity; this corresponds to motions on or close to the separatrix of the phase plane of the dynamical system.

Type
Research Article
Information
Symposium - International Astronomical Union , Volume 62: The Stability of the Solar System , 1974 , pp. 209
Copyright
Copyright © Reidel 1974 

References

Jupp, A. H.: 1972, Celes. Mech. 5, 8–26.CrossRefGoogle Scholar