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A global solution in the resonance problem of Poincaré

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Abstract

Poincaré's procedure for the construction of a global solution for a particular class of resonance problem is investigated, with particular emphasis placed on those motions corresponding to circulation in the phase space. It is demonstrated that an error on Poincaré's part leads to an impractical, yet formally acceptable, procedure.

The merits of alternative methods are discussed, with particular reference to the studies of Garfinkel and the author.

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References

  • Garfinkel, B.: 1972,Celes. Mech. 5, 189.

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  • Garfinkel, B., Jupp, A. H., and Williams, C.: 1971,Astron. J. 76, 157.

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  • Jupp, A. H.: 1969,Astron. J. 74, 35.

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  • Jupp, A. H.: 1972,Celes. Mech. 5, 8.

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  • Jupp, A. H.: 1973a,Celes. Mech. 7, 347.

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  • Jupp, A. H.: 1973b,Celes. Mech. (in press).

  • Poincaré, H.: 1893,Les méthodes nouvelles de la méchanique céleste,2, Gauthier-Villars, Paris, p. 206.

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Authors and Affiliations

  1. Dept. of Applied Mathematics, University of Liverpool, England

    Alan H. Jupp

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  1. Alan H. Jupp
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Jupp, A.H. A global solution in the resonance problem of Poincaré. Celestial Mechanics 8, 213–216 (1973). https://doi.org/10.1007/BF01231416

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  • DOI: https://doi.org/10.1007/BF01231416

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