In this paper, we consider minimizing the action functional as a method for numerically discovering periodic solutions to the n-body problem. With this method, we can find a large number of choreographies and other more general solutions. We show that most of the solutions found, including all but one of the choreographies, are unstable. It appears to be much easier to find unstable solutions to the n-body problem than stable ones. Simpler solutions are more likely to be stable than exotic ones.

Original languageEnglish (US)
Pages (from-to)422-433
Number of pages12
JournalAnnals of the New York Academy of Sciences
StatePublished - 2004

All Science Journal Classification (ASJC) codes

  • Biochemistry, Genetics and Molecular Biology(all)
  • Neuroscience(all)
  • History and Philosophy of Science


  • Action principle
  • New orbits
  • n-body problem


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