Periodic solutions of symmetric Kepler perturbations and applications |
| |
Authors: | Angelo Alberti Claudio Vidal |
| |
Institution: | 1. Departamento de Matemática, Universidade Federal de Sergipe, Cidade universitária Prof. José Aló?sio de Campos, Jardim Rosa Elze, S?o Cristov?o -SE, Brasil.angelo@ufs.br;3. Grupo de Investigación en Sistemas Dinámicos y Aplicaciones (GISDA), Departamento de Matemática, Facultad de Ciencias, Universidad del Bío-Bío, Casilla 5-C, Concepción, VIII-Región, Chile. clvidal@ubiobio.cl |
| |
Abstract: | 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 ?3. 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. |
| |
Keywords: | Perturbation theory Symmetries Continuation method Delaunay-Poincaré variables Circular Solutions |
|
|