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
Published in:Celestial mechanics and dynamical astronomy Vol. 131; no. 7; pp. 1 - 27
Main Authors: Corbera, Montserrat, Cors, Josep M., Roberts, Gareth E.
Format: Journal Article Publication
Language:English
Published: Dordrecht Springer Netherlands 01.07.2019
Springer Nature B.V
Subjects:
37 Dynamical systems and ergodic theory
37N Applications
50 years of Celestial Mechanics and Dynamical Astronomy
70 Mechanics of particles and systems
70F Dynamics of a system of particles, including celestial mechanics
Aerospace Technology and Astronautics
Astrophysics and Astroparticles
Central configuration
Classical Mechanics
Classificació AMS
Classification
Configurations
Convex central configurations
Dynamical Systems and Ergodic Theory
Enginyeria mecànica
Four body problem
Geophysics/Geodesy
Many-body problem
Matemàtiques i estadística
n-Body problem
Original Article
Physics
Physics and Astronomy
Problema dels cossos múltiples
Àrees temàtiques de la UPC
Body problem
Convex central configurations
Central configuration
ISSN:0923-2958, 1572-9478
Online Access:Get full text
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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 .
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ISSN:0923-2958
1572-9478
DOI:10.1007/s10569-019-9911-7