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

Kenneth Meyer, Qiu-Dong Wang

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13 Scopus citations


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 cordinates 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.

Original languageEnglish (US)
Pages (from-to)311-336
Number of pages26
JournalTransactions of the American Mathematical Society
Issue number1
Publication statusPublished - 1993
Externally publishedYes


ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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