On the stability of equilibria in two degrees of freedom Hamiltonian systems under resonances.
- Elipe, A. 1
- Lanchares, V. 2
- Pascual, A.I. 2
-
1
Universidad de Zaragoza
info
-
2
Universidad de La Rioja
info
ISSN: 0938-8974
Année de publication: 2005
Volumen: 15
Número: 5
Pages: 305-319
Type: Article
D'autres publications dans: Journal of Nonlinear Science
Résumé
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. © 2005 Springer Science+Business Media, Inc.