Equilateral chains and cyclic central configurations of the planar five-body problem. (English) Zbl 1502.70027
Summary: 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.
MSC:
| 70F10 | \(n\)-body problems |
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