On the Stability of Equilibria in Two-Degrees-of- Freedom Hamiltonian Systems Under Resonances |
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Authors: | A. Elipe V. Lanchares A.I. Pascual |
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Affiliation: | (1) Grupo de Mecanica Espacial, Universidad de Zaragoza, 50009 Zaragoza, Spain;(2) Dept. Matematicas y Computacion, Universidad de La Rioja, 26004 Logrono, Spain |
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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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Keywords: | Nonlinear stability Normal forms |
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