On the periodic orbits of the circular double Sitnikov problem
We introduce a restricted four body problem in a 2 + 2 configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the plane where the primaries evolve, so almost every solution is a collision orbit. We exte...
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Published in | Comptes rendus. Mathématique Vol. 347; no. 5; pp. 333 - 336 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Paris
Elsevier SAS
01.03.2009
Elsevier |
Subjects | |
Online Access | Get full text |
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Summary: | We introduce a restricted four body problem in a
2
+
2
configuration extending the classical Sitnikov problem to the Double Sitnikov problem. The secondary bodies are moving on the same perpendicular line to the plane where the primaries evolve, so almost every solution is a collision orbit. We extend the solutions beyond collisions with a symplectic regularization and study the set of energy surfaces that contain periodic orbits.
To cite this article: H. Jiménez Pérez, E.A. Lacomba, C. R. Acad. Sci. Paris, Ser. I 347 (2009).
On présente un problème à quatre corps en configuration
2
+
2
qui étend le problème de Sitnikov au problème double de Sitnikov. Dans cette configuration presque toute solution du problème est une orbite avec collisions. On étend les solutions qui présentent des collisions en utilisant une regularisation symplectique et on étudie l'ensemble des surfaces d'énergie qui contiennent des orbites périodiques.
Pour citer cet article : H. Jiménez Pérez, E.A. Lacomba, C. R. Acad. Sci. Paris, Ser. I 347 (2009). |
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ISSN: | 1631-073X 1778-3569 |
DOI: | 10.1016/j.crma.2009.01.011 |