Global phase structure of the restricted isosceles three-body problem with positive energy

Authors:
Kenneth Meyer and Qiu Dong Wang

Journal:
Trans. Amer. Math. Soc. **338** (1993), 311-336

MSC:
Primary 70F07; Secondary 58F40

DOI:
https://doi.org/10.1090/S0002-9947-1993-1136546-1

MathSciNet review:
1136546

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Abstract: We study a restricted three-body problem with special symmetries: the restricted isosceles three-body problem. For positive energy the energy manifold is partially compactified by adding boundary manifolds corresponding to infinity and triple collision. We use a new set of coordinates which are a variation on the McGehee coordinates of celestial mechanics. These boundary manifolds are used to study the global phase structure of this gradational system. The orbits are classified by intersection number, that is the number of times the infinitesimal body cross the line of syzygy before escaping to infinity.

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DOI:
https://doi.org/10.1090/S0002-9947-1993-1136546-1

Article copyright:
© Copyright 1993
American Mathematical Society