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04 December 2021
  » arxiv » 1104.2288

 Article overview

Variational approach to second species periodic solutions of Poincar'e of the 3 body problem
Sergey Bolotin ; Piero Negrini ;
Date 12 Apr 2011
AbstractWe consider the plane 3 body problem with 2 of the masses small. Periodic solutions with near collisions of small bodies were named by Poincar’e second species periodic solutions. Such solutions shadow chains of collision orbits of 2 uncoupled Kepler problems. Poincar’e only sketched the proof of the existence of second species solutions. Rigorous proofs appeared much later and only for the restricted 3 body problem. We develop a variational approach to the existence of second species periodic solutions for the nonrestricted 3 body problem. As an application, we give a rigorous proof of the existence of a class of second species solutions.
Source arXiv, 1104.2288
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