Journal of Nonlinear Mathematical Physics

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Volume 23, Issue 3, June 2016, Pages 439 - 465

Periodic solutions of symmetric Kepler perturbations and applications

Authors
Angelo Alberti*
Departamento de Matemática, Universidade Federal de Sergipe, Cidade universitária Prof. José Alóısio de Campos, Jardim Rosa Elze, São Cristovão -SE, Brasil,angelo@ufs.br
Claudio Vidal†
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
*

The first author was partially supported by a CNPq post-doc fellowship Grant No. 233145/2014-1.

†

Partially supported by Fondecyt 1130644 and CONICYT/Project MATH-AMSUD, 14 MATH-02.

Received 27 January 2016, Accepted 9 February 2016, Available Online 6 January 2021.
DOI
10.1080/14029251.2016.1204721How to use a DOI?
Keywords
Perturbation theory; Symmetries; Continuation method; Delaunay-Poincaré variables; Circular Solutions
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 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.

Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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<Previous Article In Issue
Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
23 - 3
Pages
439 - 465
Publication Date
2021/01/06
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2016.1204721How to use a DOI?
Copyright
© 2016 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

risenwbib
TY  - JOUR
AU  - Angelo Alberti
AU  - Claudio Vidal
PY  - 2021
DA  - 2021/01/06
TI  - Periodic solutions of symmetric Kepler perturbations and applications
JO  - Journal of Nonlinear Mathematical Physics
SP  - 439
EP  - 465
VL  - 23
IS  - 3
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2016.1204721
DO  - 10.1080/14029251.2016.1204721
ID  - Alberti2021
ER  -