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 language | English (US) |
|---|---|
| Article number | 4 |
| Journal | Journal of Nonlinear Science |
| Volume | 33 |
| Issue number | 1 |
| DOIs | |
| State | Published - 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