Home > Articles > Published articles > On the equilateral pentagonal central configurations |
Date: | 2022 |
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 5-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. |
Grants: | Agencia Estatal de Investigación PID2019-104658GB-I00 European Commission 777911 |
Rights: | Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades. |
Language: | Anglès |
Document: | Article ; recerca ; Versió acceptada per publicar |
Subject: | Central configuration ; 5-body problem ; Equilateral pentagon |
Published in: | Communications in nonlinear science and numerical simulation, Vol. 112 (September 2022) , art. 106511, ISSN 1007-5704 |
Available from: 2024-09-30 Postprint |