Central configurations of the 4-body problem with masses m<inf>1</inf> = m<inf>2</inf> &gt; m<inf>3</inf> = m<inf>4</inf> = m &gt; 0 and m small

Montserrat Corbera, Jaume Llibre

Research output: Contribution to journalArticleResearchpeer-review

10 Citations (Scopus)

Abstract

In this paper we give a complete description of the families of central configurations of the planar 4-body problem with two pairs of equals masses and two equal masses sufficiently small. In particular, we give an analytical proof that this particular 4-body problem has exactly 34 different classes of central configurations. Moreover for this problem we prove the following two conjectures: There is a unique convex planar central configuration of the 4-body problem for each ordering of the masses in the boundary of its convex hull, which appears in Albouy and Fu (2007) [3]. We also prove the conjecture: There is a unique convex planar central configuration having two pairs of equal masses located at the adjacent vertices of the configuration and it is an isosceles trapezoid. Finally, the families of central configurations of this 4-body problem are numerically continued to the 4-body problem with four equal masses. © 2014 Elsevier Inc. All rights reserved.
Original languageEnglish
Pages (from-to)121-147
JournalApplied Mathematics and Computation
Volume246
DOIs
Publication statusPublished - 1 Nov 2014

Keywords

  • 4-body problem
  • Central configurations
  • Convex central configurations
  • Trapezoidal central configurations
  • Two-small masses

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