scholarly journals On bifurcations and stability of central configurations in the planar circular restricted four-body problem

2021 ◽  
Vol 1959 (1) ◽  
pp. 012006
Author(s):  
B S Bardin ◽  
E V Volkov
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Four Body Problem

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.

scholarly journals Bifurcations of Central Configurations in the Four-Body Problem with Some Equal Masses

2016 ◽  
Vol 15 (1) ◽  
pp. 440-458 ◽  
Author(s):  
David Rusu ◽  
Manuele Santoprete
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Four Body Problem

scholarly journals Symmetry of planar four-body convex central configurations

2008 ◽  
Vol 464 (2093) ◽  
pp. 1355-1365 ◽  
Author(s):  
Alain Albouy ◽  
Yanning Fu ◽  
Shanzhong Sun
Keyword(s):  
Body Problem ◽  
The Other ◽  
Central Configurations ◽  
Central Configuration ◽  
Geometric Properties ◽  
Four Body Problem ◽  
Planar Central Configurations ◽  
The Masses ◽  
The Relationship ◽  
Convex Central Configuration

We study the relationship between the masses and the geometric properties of central configurations. We prove that, in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal. If these two masses are unequal, then the less massive one is closer to the former diagonal. Finally, we extend these results to the case of non-planar central configurations of five particles.

The Set of Degenerate Central Configurations in the Planar Restricted Four-Body Problem

2011 ◽  
Vol 43 (2) ◽  
pp. 634-661 ◽  
Author(s):  
Jean F. Barros ◽  
Eduardo S. G. Leandro
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Four Body Problem

scholarly journals Central configurations for the planar Newtonian four-body problem

2010 ◽  
Vol 108 (1) ◽  
pp. 73-93 ◽  
Author(s):  
E. Piña ◽  
P. Lonngi
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Four Body Problem

Isosceles trapezoid central configurations of the Newtonian four-body problem

2012 ◽  
Vol 142 (3) ◽  
pp. 665-672 ◽  
Author(s):  
Zhifu Xie
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Central Configuration ◽  
Basic Method ◽  
One Dimensional ◽  
Isosceles Trapezoid ◽  
Four Body Problem ◽  
Explicit Expressions

We use a simple direct and basic method to prove that there is a unique isosceles trapezoid central configuration of the planar Newtonian four-body problem when two pairs of equal masses are located at adjacent vertices of a trapezoid. Such isosceles trapezoid central configurations are an exactly one-dimensional family. Explicit expressions for masses are given in terms of the size of the quadrilateral.

scholarly journals On the central configurations of the planar restricted four-body problem

2006 ◽  
Vol 226 (1) ◽  
pp. 323-351 ◽  
Author(s):  
Eduardo S.G. Leandro
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Four Body Problem
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