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On the Stability of Equilibria in Two-Degrees-of- Freedom Hamiltonian Systems Under Resonances

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Abstract

We consider the problem of stability of equilibrium points in Hamiltonian systems of two degrees of freedom under resonances. Determining the stability or instability is based on a geometrical criterion based on how two surfaces, related with the normal form, intersect one another. The equivalence of this criterion with a result of Cabral and Meyer is proved. With this geometrical procedure, the hypothesis may be extended to more general cases.

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Authors and Affiliations

  1. Grupo de Mecanica Espacial, Universidad de Zaragoza, 50009 Zaragoza, Spain

    A. Elipe

  2. Dept. Matematicas y Computacion, Universidad de La Rioja, 26004 Logrono, Spain

    V. Lanchares & A.I. Pascual

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  1. A. Elipe
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  2. V. Lanchares
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  3. A.I. Pascual
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Correspondence to V. Lanchares.

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Elipe, A., Lanchares, V. & Pascual, A. On the Stability of Equilibria in Two-Degrees-of- Freedom Hamiltonian Systems Under Resonances. J Nonlinear Sci 15, 305–319 (2005). https://doi.org/10.1007/s00332-004-0674-1

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  • DOI: https://doi.org/10.1007/s00332-004-0674-1

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