Combined effects of radiation and oblateness on the existence and stability of equilibrium points in the perturbed restricted four-body problem

2017 ◽  
Vol 4 (3) ◽  
pp. 174 ◽  
Author(s):  
Jagadish Singh ◽  
Aguda Ekele Vincent
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Combined Effects ◽  
Stability Of Equilibrium ◽  
Existence And Stability ◽  
Four Body Problem ◽  
Effects Of Radiation

Nonlinear Stability of Equilibrium Points in the Planar Equilateral Restricted Mass-Unequal Four-Body Problem

2021 ◽  
Vol 31 (11) ◽  
pp. 2130031
Author(s):  
José Alejandro Zepeda Ramírez ◽  
Martha Alvarez-Ramírez ◽  
Antonio García
Keyword(s):  
Nonlinear Stability ◽  
Mass Formula ◽  
Body Problem ◽  
Equilibrium Points ◽  
Constant Angular Velocity ◽  
Gravitational Attraction ◽  
Stability Of Equilibrium ◽  
Four Body Problem ◽  
Elliptic Equilibrium ◽  
The Stability

In this paper, we investigate the stability of equilibrium points for the planar restricted equilateral four-body problem in the case that one particle of negligible mass is moving under the Newtonian gravitational attraction of three positive masses [Formula: see text], [Formula: see text] and [Formula: see text] (called primaries). These always lie at the vertices of an equilateral triangle (Lagrangian configuration) and move with constant angular velocity in circular orbits around their center of masses. We consider the case where all the primaries have unequal masses, and investigate the nonlinear stability (in the sense of Lyapunov) of the elliptic equilibrium for the specific values of the mass [Formula: see text] and [Formula: see text] of the primary, fixed on the horizontal axis. Moreover, the [Formula: see text][Formula: see text]:[Formula: see text][Formula: see text] four-order resonant cases are determined and the stability is investigated. In this study, Markeev’s theorem and Arnold’s theorem become key ingredients.

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