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

2017 ◽  
Vol 129 (3) ◽  
pp. 321-328 ◽  
Author(s):  
J. Lino Cornelio ◽  
M. Álvarez–Ramírez ◽  
Josep M. Cors
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Stacked Central Configurations

scholarly journals Stacked central configurations for the spatial six-body problem

2009 ◽  
Vol 59 (9) ◽  
pp. 1216-1226 ◽  
Author(s):  
Luis Fernando Mello ◽  
Felipe Emanoel Chaves ◽  
Antonio Carlos Fernandes ◽  
Braulio Augusto Garcia
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Stacked Central Configurations

scholarly journals New stacked central configurations for the planar 5-body problem

2011 ◽  
Vol 110 (1) ◽  
pp. 43-52 ◽  
Author(s):  
Jaume Llibre ◽  
Luis Fernando Mello ◽  
Ernesto Perez-Chavela
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Stacked Central Configurations

scholarly journals Stacked Central Configurations for the Spatial Nine-Body Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Su Xia ◽  
Deng Chunhua
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Stacked Central Configurations

We show the existence of the twisted stacked central configurations for the 9-body problem. More precisely, the position vectorsx1,x2,x3,x4, andx5are at the vertices of a square pyramidΣ; the position vectorsx6,x7,x8, andx9are at the vertices of a squareΠ.

Stacked Central Configurations for the Spatial Seven–Body Problem

2012 ◽  
Vol 12 (1) ◽  
pp. 101-114 ◽  
Author(s):  
Luis Fernando Mello ◽  
Antonio Carlos Fernandes
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Stacked 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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