A family of stacked central configurations in the planar five-body problem

We study planar central configurations of the five-body problem where three bodies, m 1 , m 2 and m 3 , are collinear and ordered from left to right, while the other two, m 4 and m 5 , are placed symmetrically with respect to the line containing the three collinear bodies. We prove that when the col...

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Bibliographic Details
Published in:Celestial mechanics and dynamical astronomy Vol. 129; no. 3; pp. 321 - 328
Main Authors: Cornelio, J. Lino, Álvarez–Ramírez, M., Cors, Josep M.
Format: Journal Article Publication
Language:English
Published: Dordrecht Springer Netherlands 01.11.2017
Springer Nature B.V
Subjects:
70 Mechanics of particles and systems
70F Dynamics of a system of particles, including celestial mechanics
Aerospace Technology and Astronautics
Astrophysics
Astrophysics and Astroparticles
Celestial mechanics
Central configurations
Chaos theory
Classical Mechanics
Classificació AMS
Collinearity
Configurations
Dynamical Systems and Ergodic Theory
Enginyeria mecànica
Geophysics/Geodesy
Many-body problem
Matemàtiques i estadística
Mecànica celest
Original Article
Physics
Physics and Astronomy
Planar five-body problem
Problema dels cossos múltiples
Stacked central configurations
Three body problem
Àrees temàtiques de la UPC
Central configurations
Stacked central configurations
Planar five-body problem
ISSN:0923-2958, 1572-9478
Online Access:Get full text
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Description
Summary:We study planar central configurations of the five-body problem where three bodies, m 1 , m 2 and m 3 , are collinear and ordered from left to right, while the other two, m 4 and m 5 , are placed symmetrically with respect to the line containing the three collinear bodies. We prove that when the collinear bodies form an Euler central configuration of the three-body problem with m 1 = m 3 , there exists a new family, missed by Gidea and Llibre (Celest Mech Dyn Astron 106:89–107, 2010 ), of stacked five-body central configuration where the segments m 4 m 5 and m 1 m 3 do not intersect.
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ISSN:0923-2958
1572-9478
DOI:10.1007/s10569-017-9782-8