On the equilateral pentagonal central configurations

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...

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Detalhes bibliográficos
Autores: Álvarez Ramírez, Martha|||0000-0001-9187-1757, Gasull, Armengol|||0000-0002-1719-8231, Llibre, Jaume|||0000-0002-9511-5999
Formato: artículo
Fecha de publicación:2022
País:España
Recursos:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:259916
Acesso em linha:https://ddd.uab.cat/record/259916
https://dx.doi.org/urn:doi:10.1016/j.cnsns.2022.106511
Access Level:acceso abierto
Palavra-chave:Central configuration
5-body problem
Equilateral pentagon
Descrição
Resumo: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.