On the equilateral pentagonal central configurations
Dynamical Systems
2022-05-25 v1 Mathematical Physics
Classical Analysis and ODEs
math.MP
Abstract
An equilateral pentagon is a polygon in the plane with five sides of equal length. In this paper we classify the central configurations of the -body problem having the five bodies at the vertices of an equilateral pentagon with an axis of symmetry. We prove that there are two unique classes of such equilateral pentagons providing central configurations, one concave equilateral pentagon and one convex equilateral pentagon, the regular one. A key point of our proof is the use of rational parameterizations to transform the corresponding equations, which involve square roots, into polynomial equations.
Keywords
Cite
@article{arxiv.2204.03808,
title = {On the equilateral pentagonal central configurations},
author = {Martha Alvarez-Ramírez and Armengol Gasull and Jaume Llibre},
journal= {arXiv preprint arXiv:2204.03808},
year = {2022}
}