Classifying four-body convex central configurations

We classify the full set of convex central configurations in the Newtonian planar four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include kite, trapezoidal, co-circular, equidiagonal, orthodi...

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Bibliographic Details
Authors: Corbera Subirana, Montserrat|||0000-0002-0367-9667, Cors Iglesias, Josep Maria|||0000-0002-9803-8490, Roberts, Gareth E.
Format: article
Publication Date:2019
Country:España
Institution:Universitat Autònoma de Barcelona
Repository:Dipòsit Digital de Documents de la UAB
Language:English
OAI Identifier:oai:ddd.uab.cat:236637
Online Access:https://ddd.uab.cat/record/236637
https://dx.doi.org/urn:doi:10.1007/s10569-019-9911-7
Access Level:Open access
Keyword:Central configuration
N-Body problem
Convex central configurations
Description
Summary:We classify the full set of convex central configurations in the Newtonian planar four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property. Special cases considered include kite, trapezoidal, co-circular, equidiagonal, orthodiagonal, and bisecting-diagonal configurations. Good coordinates for describing the set are established. We use them to prove that the set of four-body convex central configurations with positive masses is three-dimensional, a graph over a domain D that is the union of elementary regions in R+3.