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



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.


Hamiltonian systems 2 + 2-Body problem Sitnikov problem Celestial mechanics 

Mathematics Subject Classification (2000)

Primary 70F10 70F16 Secondary 37J99 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversidad Autonoma Metropolitana, IztapalapaIztapalapa, Mexico CityMexico

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