Homographic solutions of the n-body problem in E4

Julian I. Palmore

Research output: Contribution to journalArticle

Abstract

We prove the existence of many homographic solutions of the n-body problem in E4 by topological methods. Homographic solutions are associated with relative equilibria. Homothetic solutions always give rise to central configurations. In Euclidean space E4 central configurations are a proper subset of the relative equilibria for any n ≥ 3 and for any (mi)ε{lunate}R+n. We compare the existence and classification of homographic solutions of the n-body problem in E3 with the Newtonian potential and that of homographic solutions of the n-body problem in E4. Classifying relative equilibria leads to classifying homographic solutions.

Original languageEnglish (US)
Pages (from-to)279-290
Number of pages12
JournalJournal of Differential Equations
Volume40
Issue number2
DOIs
StatePublished - May 1981

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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