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A simple generalization of wisdom's perturbative method

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Abstract

A simple generalization of Wisdom's perturbative method, as originally proposed by Wisdom (1985), is obtained. Any number of resonant cosines can be handled and the method can also accommodate more involved disturbing functions. Averaged trajectories are easily obtained by drawing level curves of the action. Here, the method is first tested for simple models of 3:1 and 2:1 resonant problems. Comparisons with numerical integration and surface-section curves show very good agreements.

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Author notes

  1. Tadashi Yokoyama

    Present address: Universidade Estadual Paulista IGCE-DEMAC, Caixa Postal 178, CEP 13500-970, Rio Claro, Estado de São Paulo, Brazil

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  1. Departamento de Estatística Matemática Aplicada e Computacional, Universidade Estadual Paulista, Rio Claro, Brazil

    Tadashi Yokoyama

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  1. Tadashi Yokoyama
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Yokoyama, T. A simple generalization of wisdom's perturbative method. Celestial Mech Dyn Astr 64, 243–260 (1996). https://doi.org/10.1007/BF00728350

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  • DOI: https://doi.org/10.1007/BF00728350

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