The effect of perturbations in coriolis and centrifugal forces on the nonlinear stability of equilibrium points in the restricted problem of three bodies

1983 ◽  
Vol 30 (1) ◽  
pp. 97-114 ◽  
Author(s):  
K. B. Bhatnagar ◽  
P. P. Hallan
Keyword(s):  
Nonlinear Stability ◽  
Restricted Problem ◽  
Equilibrium Points ◽  
Centrifugal Forces ◽  
Stability Of Equilibrium ◽  
Coriolis And Centrifugal Forces

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.

scholarly journals Effect of Perturbations in Coriolis and Centrifugal Forces on the Nonlinear Stability of Equilibrium Point in Robe's Restricted Circular Three-Body Problem

2008 ◽  
Vol 2008 ◽  
pp. 1-21 ◽  
Author(s):  
P. P. Hallan ◽  
Khundrakpam Binod Mangang
Keyword(s):  
Equilibrium Point ◽  
Nonlinear Stability ◽  
Body Problem ◽  
Kam Theory ◽  
Density Parameter ◽  
Centrifugal Forces ◽  
Three Body Problem ◽  
Coriolis And Centrifugal Forces ◽  
Mass Ratios ◽  
Three Body

The effect of perturbations in Coriolis and cetrifugal forces on the nonlinear stability of the equilibrium point of the Robe's (1977) restricted circular three-body problem has been studied when the density parameterKis zero. By applying Kolmogorov-Arnold-Moser (KAM) theory, it has been found that the equilibrium point is stable for all mass ratiosμin the range of linear stability8/9+(2/3)((43/25)ϵ1−(10/3)ϵ)<μ<1, whereϵandϵ1are, respectively, the perturbations in Coriolis and centrifugal forces, except for five mass ratiosμ1=0.93711086−1.12983217ϵ+1.50202694ϵ1,μ2=0.9672922−0.5542091ϵ+1.2443968ϵ1,μ3=0.9459503−0.70458206ϵ+1.28436549ϵ1,μ4=0.9660792−0.30152273ϵ+ 1.11684064ϵ1,μ5=0.893981−2.37971679ϵ+ 1.22385421ϵ1, where the theory is not applicable.

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