Equilateral Chains and Cyclic Central Configurations of the Planar Five-Body Problem

Yiyang Deng, Marshall Hampton

Research output: Contribution to journalArticlepeer-review

Abstract

Central configurations and relative equilibria are an important facet of the study of the N-body problem, but become very difficult to rigorously analyze for N> 3. In this paper, we focus on a particular but interesting class of configurations of the five-body problem: the equilateral pentagonal configurations, which have a cycle of five equal edges. We prove a variety of results concerning central configurations with this property, including a computer-assisted proof of the finiteness of such configurations for any positive five masses with a range of rational-exponent homogeneous potentials (including the Newtonian case and the point-vortex model), some constraints on their shapes, and we determine some exact solutions for particular N-body potentials.

Original languageEnglish (US)
Article number4
JournalJournal of Nonlinear Science
Volume33
Issue number1
DOIs
StatePublished - Feb 2023

Bibliographical note

Funding Information:
The authors would like to thank Manuele Santoprete for the suggestion to study this class of configuration. Yiyang Deng was partially supported by the Mathematics and Statistics Team from Chongqing Technology and Business University (ZDPTTD201906).

Funding Information:
The authors would like to thank Manuele Santoprete for the suggestion to study this class of configuration. Yiyang Deng was partially supported by the Mathematics and Statistics Team from Chongqing Technology and Business University (ZDPTTD201906).

Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.

Keywords

  • Celestial mechanics
  • Central configurations
  • N-body problem
  • Relative equilibria

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