homographic solutions
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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.


2013 ◽  
Vol 30 (2) ◽  
pp. 353-360 ◽  
Author(s):  
Abdalla M. Mansur ◽  
Daniel C. Offin

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Yiming Long

AbstractIt is well known that the linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three-body problem depends on the mass parameter β = 27(m


2011 ◽  
Vol 250 (1) ◽  
pp. 340-366 ◽  
Author(s):  
Florin Diacu ◽  
Ernesto Pérez-Chavela

2011 ◽  
Author(s):  
E. A. Grebenikov ◽  
D. M. Diarova ◽  
N. I. Zemtsova

2007 ◽  
Vol 99 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Mercedes Arribas ◽  
Antonio Elipe ◽  
Tilemahos Kalvouridis ◽  
Manuel Palacios

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