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Energy Levels of Periodic Solutions of the Circular 2 + 2 Sitnikov Problem

2009; Birkhäuser; Volume: 8; Issue: 1 Linguagem: Inglês

10.1007/s12346-009-0003-z

1662-3592

Hugo Jiménez-Pérez, Ernesto A. Lacomba,

Stellar, planetary, and galactic studies

We introduce a restricted four body problem in a 2 + 2 configuration extending the classical circular Sitnikov problem to the circular double Sitnikov problem. Since the secondary bodies are moving on the perpendicular line to the plane where the primaries evolve, 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.