scholarly journals On the Existence of Central Configurations of p Nested n-gons

2009 ◽  
Vol 8 (2) ◽  
pp. 255-265 ◽  
Author(s):  
Montserrat Corbera ◽  
Joaquin Delgado ◽  
Jaume Llibre
Keyword(s):  
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.

Central configurations of the five-body problem with two isosceles triangles

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Antonio Carlos Fernandes ◽  
Braulio Augusto Garcia ◽  
Luis Fernando Mello ◽  
Lucas Ruiz dos Santos
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Isosceles Triangles

Convex but not Strictly Convex Central Configurations

2017 ◽  
Vol 30 (4) ◽  
pp. 1427-1438 ◽  
Author(s):  
Antonio Carlos Fernandes ◽  
Braulio Augusto Garcia ◽  
Luis Fernando Mello
Keyword(s):  
Central Configurations ◽  
Strictly Convex

Central configurations of four bodies with an axis of symmetry

2016 ◽  
Vol 125 (1) ◽  
pp. 33-70 ◽  
Author(s):  
Bálint Érdi ◽  
Zalán Czirják
Keyword(s):  
Central Configurations ◽  
Axis Of Symmetry
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