A Four-Body Convex Central Configuration with Perpendicular Diagonals is Necessarily a Kite

We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem.

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Bibliographic Details
Published in:Qualitative theory of dynamical systems Vol. 17; no. 2; pp. 367 - 374
Main Authors: Corbera, Montserrat, Cors, Josep M., Roberts, Gareth E.
Format: Journal Article Publication
Language:English
Published: Cham Springer International Publishing 01.07.2018
Springer Nature B.V
Subjects:
37 Dynamical systems and ergodic theory
37N Applications
70 Mechanics of particles and systems
70F Dynamics of a system of particles, including celestial mechanics
Central configuration
Classificació AMS
Configurations
Difference and Functional Equations
Dynamical Systems and Ergodic Theory
Enginyeria mecànica
Many-body problem
Matemàtiques i estadística
Mathematics
Mathematics and Statistics
n-Body problem
n-Vortex problem
Problema dels cossos múltiples
Àrees temàtiques de la UPC
Body problem
70F10
Central configuration
Vortex problem
70F15
37N05
ISSN:1575-5460, 1662-3592
Online Access:Get full text
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Description
Summary:We prove that any four-body convex central configuration with perpendicular diagonals must be a kite configuration. The result extends to general power-law potential functions, including the planar four-vortex problem.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1575-5460
1662-3592
DOI:10.1007/s12346-017-0238-z