Non linear stability in resonant cases: A geometrical approach.
- Elipe, A. 2
- Lanchares, V. 1
- López-Moratalla, T. 3
- Riaguas, A. 22
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1
Universidad de La Rioja
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2
Universidad de Zaragoza
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- 3 Real Inst. y Observ. de la Armada, 11110 San Fernando, Spain
ISSN: 0938-8974
Año de publicación: 2001
Volumen: 11
Número: 3
Páginas: 211-222
Tipo: Artículo
beta Ver similares en nube de resultadosOtras publicaciones en: Journal of Nonlinear Science
Resumen
In systems with two degrees of freedom, Arnold's theorem is used for studying nonlinear stability of the origin when the quadratic part of the Hamiltonian is a nondefinite form. In that case, a previous normalization of the higher orders is needed, which reduces the Hamiltonian to homogeneous polynomials in the actions. However, in the case of resonances, it could not be possible to bring the Hamiltonian to the normal form required by Arnold's theorem. In these cases, we determine the stability from analysis of the normalized phase flow. Normalization up to an arbitrary order by Lie-Deprit transformation is carried out using a generalization of the Lissajous variables.