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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Global phase structure of the restricted isosceles three-body problem with positive energy
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by Kenneth Meyer and Qiu Dong Wang PDF
Trans. Amer. Math. Soc. 338 (1993), 311-336 Request permission

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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Additional Information
  • © Copyright 1993 American Mathematical Society
  • 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