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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
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: http://dx.doi.org/10.1090/S0002-9947-1993-1136546-1
PII: S 0002-9947(1993)1136546-1
Article copyright: © Copyright 1993 American Mathematical Society