On the stability of equilibria in two-degrees-of-freedom Hamiltonian systems under resonances

被引：16
|
作者：
Elipe, A [1 ]
Lanchares, V
Pascual, AI
机构：
[1] Univ Zaragoza, Grp Mecan Espacial, E-50009 Zaragoza, Spain
[2] Univ La Rioja, Dept Matemat & Comp, Logrono 26004, Spain
来源：
JOURNAL OF NONLINEAR SCIENCE | 2005年 / 15卷 / 05期
关键词：
nonlinear stability; normal forms;
D O I：
10.1007/s00332-004-0674-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：305 / 319
页数：15
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