On the existence of bi-pyramidal central configurations of the n + 2-body problem with an n-gon base

Montserrat Corbera, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

1 Citation (Scopus)

Abstract

In this paper we prove the existence of central configurations of the n + 2-body problem where n equal masses are located at the vertices of a regular n-gon and the remaining 2 masses, which are not necessarily equal, are located on the straight line orthogonal to the plane containing the n-gon passing through its center. Here this kind of central configurations is called bi-pyramidal central configurations. In particular, we prove that if the masses mn+1 and mn+2 and their positions satisfy convenient relations, then the configuration is central. We give explicitly those relations.
Original languageEnglish
Pages (from-to)1049-1060
JournalDiscrete and Continuous Dynamical Systems
Volume33
Issue number3
DOIs
Publication statusPublished - 1 Jan 2013

Keywords

  • Bi-pyramidal central configurations
  • N+2-body problem
  • Spatial central configurations

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