Periodic orbits for the planar Newtonian three-body problem coming from the elliptic restricted three-body problems

Llibre, Jaume; Saari, Donald G.

doi:10.1090/S0002-9947-1995-1297534-X

Periodic orbits for the planar Newtonian three-body problem coming from the elliptic restricted three-body problems
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by Jaume Llibre and Donald G. Saari PDF

Trans. Amer. Math. Soc. 347 (1995), 3017-3030 Request permission

Abstract:

Through the introduction of a new coordinate system followed by a Poincaré compactification, a new relationship is developed to connect the planar three-body problem with the various planar restricted three-body systems. This framework is further used to develop new conditions for the continuation of symmetric periodic orbits from elliptic restricted systems to the full planar three-body problem.

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