Spatial central configurations for the 1+4 body problem

2002 ◽  
pp. 1-16 ◽  
Author(s):  
Alain Albouy ◽  
Jaume Llibre
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Spatial Central Configurations

scholarly journals New Classes of Spatial Central Configurations forN+N+ 2-Body Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Liu Xuefei ◽  
Zhang Chuntao ◽  
Luo Jianmei ◽  
Zhang Gan
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Spatial Central Configurations

scholarly journals New classes of spatial central configurations for the 7-body problem

2014 ◽  
Vol 86 (1) ◽  
pp. 3-9
Author(s):  
ANTONIO CARLOS FERNANDES ◽  
LUIS FERNANDO MELLO
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Equilateral Triangles ◽  
Spatial Central Configurations

In this paper we show the existence of new families of spatial central configurations for the 7-body problem. In the studied spatial central configurations, six bodies are at the vertices of two equilateral triangles , and one body is located out of the parallel distinct planes containing and . The results have simple and analytic proofs.

scholarly journals New spatial central configurations in the 5-body problem

2011 ◽  
Vol 83 (3) ◽  
pp. 763-774 ◽  
Author(s):  
Luis F. Mello ◽  
Antonio C. Fernandes
Keyword(s):  
Equilateral Triangle ◽  
Body Problem ◽  
The Other ◽  
Central Configurations ◽  
Line Passing ◽  
Spatial Central Configurations ◽  
Two Bodies

In this paper we show the existence of new families of convex and concave spatial central configurations for the 5-body problem. The bodies studied here are arranged as follows: three bodies are at the vertices of an equilateral triangle T, and the other two bodies are on the line passing through the barycenter of T that is perpendicular to the plane that contains T.

scholarly journals On the spatial central configurations of the 5--body problem and their bifurcations

2008 ◽  
Vol 1 (4) ◽  
pp. 505-518 ◽  
Author(s):  
Martha Alvarez ◽  
◽  
Joaquin Delgado ◽  
Jaume Llibre ◽  
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Spatial Central Configurations

scholarly journals Central Configurations and Action Minimizing Orbits in Kite Four-Body Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
B. Benhammouda ◽  
A. Mansur ◽  
M. Shoaib ◽  
I. Szücs-Csillik ◽  
D. Offin
Keyword(s):  
Cross Sections ◽  
Body Problem ◽  
Mass Parameter ◽  
Central Configurations ◽  
Continuous Family ◽  
Classical Action ◽  
Dynamical Aspect ◽  
Homographic Solutions ◽  
Four Body Problem ◽  
Current Article

In the current article, we study the kite four-body problems with the goal of identifying global regions in the mass parameter space which admits a corresponding central configuration of the four masses. We consider two different types of symmetrical configurations. In each of the two cases, the existence of a continuous family of central configurations for positive masses is shown. We address the dynamical aspect of periodic solutions in the settings considered and show that the minimizers of the classical action functional restricted to the homographic solutions are the Keplerian elliptical solutions. Finally, we provide numerical explorations via Poincaré cross-sections, to show the existence of periodic and quasiperiodic solutions within the broader dynamical context of the four-body problem.

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