Periodic solutions of symmetric Kepler perturbations and applications

被引：0
作者：
Angelo Alberti
Claudio Vidal
机构：
[1] Universidade Federal de Sergipe,Departamento de Matemática
[2] Universidad del Bío-Bío,Grupo de Investigación en Sistemas Dinámicos y Aplicaciones (GISDA), Departamento de Matemática, Facultad de Ciencias
来源：
Journal of Nonlinear Mathematical Physics | 2016年 / 23卷
关键词：
Perturbation theory; Symmetries; Continuation method; Delaunay-Poincaré variables; Circular Solutions; 34C25; 34C14;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We investigate the existence of several families of symmetric periodic solutions as continuation of circular orbits of the Kepler problem for certain symmetric differentiable perturbations using an appropriate set of Poincaré-Delaunay coordinates which are essential in our approach. More precisely, we try separately two situations in an independent way, namely, when the unperturbed part corresponds to a Kepler problem in inertial cartesian coordinates and when it corresponds to a Kepler problem in rotating coordinates on ℝ3. Moreover, the characteristic multipliers of the symmetric periodic solutions are characterized. The planar case arises as a particular case. Finally, we apply these results to study the existence and stability of periodic orbits of the Matese-Whitman Hamiltonian and the generalized Størmer model.
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页码：439 / 465
页数：26
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