On the Uniqueness of Co-circular Four Body Central Configurations

2021 ◽  
Vol 240 (2) ◽  
pp. 971-985
Author(s):  
Manuele Santoprete
2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
B. Benhammouda ◽  
A. Mansur ◽  
M. Shoaib ◽  
I. Szücs-Csillik ◽  
D. Offin

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.


Author(s):  
Antonio Carlos Fernandes ◽  
Braulio Augusto Garcia ◽  
Luis Fernando Mello ◽  
Lucas Ruiz dos Santos

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

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

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