Combined effect of small perturbations in the Coriolis and centrifugal forces and three-body interaction on the existence of stationary points in the R3BP

New Astronomy ◽  
2021 ◽  
pp. 101630
Author(s):  
Md Sanam Suraj ◽  
Rajiv Aggarwal ◽  
Vipin Kumar Aggarwal ◽  
Md Chand Asique
Keyword(s):  
Combined Effect ◽  
Stationary Points ◽  
Centrifugal Forces ◽  
Small Perturbations ◽  
Body Interaction ◽  
Coriolis And Centrifugal Forces ◽  
Three Body

scholarly journals Existence and linear stability of triangular points in the perturbed relativistic R3BP when the bigger primary is an oblate spheroid

2016 ◽  
Vol 4 (1) ◽  
pp. 49
Author(s):  
Bello Nakone ◽  
Jagadish Singh
Keyword(s):  
Linear Stability ◽  
Centrifugal Force ◽  
Critical Mass ◽  
Oblate Spheroid ◽  
Centrifugal Forces ◽  
Mass Ratio ◽  
Small Perturbations ◽  
Coriolis Forces ◽  
Triangular Points ◽  
Coriolis And Centrifugal Forces

We study the effects of oblateness and small perturbations in the Coriolis and centrifugal forces on the locations and stability of the triangular points in the relativistic R3BP. It is observed that the positions are affected by the oblateness, relativistic, and a small perturbation in the centrifugal force, but are unaffected by that of Coriolis force. It is also seen that the relativistic terms, oblateness, small perturbations in the centrifugal and Coriolis forces influence the critical mass ratio. It is also noticed that all the former three and the latter one possess destabilizing and stabilizing behavior respectively. However, the range of stability increases or decreases according to as p >0 or p<0 where p depends upon the relativistic, oblateness and small perturbations in the Coriolis and centrifugal forces.

scholarly journals On the perturbed restricted three-body problem

2016 ◽  
Vol 1 (1) ◽  
pp. 123-144 ◽  
Author(s):  
Elbaz I. Abouelmagd ◽  
Juan L.G. Guirao
Keyword(s):  
Linear Stability ◽  
Periodic Orbits ◽  
Body Problem ◽  
Analytical Study ◽  
Restricted Three Body Problem ◽  
Centrifugal Forces ◽  
Three Body Problem ◽  
Survey Paper ◽  
Coriolis And Centrifugal Forces ◽  
Three Body

AbstractIn this survey paper we offer an analytical study regarding the perturbed planar restricted three-body problem in the case that the three involved bodies are oblate. The existence of libration points and their linear stability are explored under the effects of the perturbations in Coriolis and centrifugal forces. The periodic orbits around these points are also studied under these effects. Moreover, the elements of periodic orbits around these points are determined.

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.

scholarly journals On the stability of L4,5 in the perturbed relativistic R3BP with a triaxial bigger primary

2016 ◽  
Vol 4 (2) ◽  
pp. 76
Author(s):  
Bello Nakone ◽  
Jagadish Singh
Keyword(s):  
Centrifugal Force ◽  
Small Perturbation ◽  
Coriolis Force ◽  
Stability Region ◽  
Centrifugal Forces ◽  
Small Perturbations ◽  
Triangular Points ◽  
Relativistic Factor ◽  
Coriolis And Centrifugal Forces ◽  
The Stability

In the present paper, we endeavor to study the stability of triangular points under the influence of small perturbations in the Coriolis and centrifugal forces, together with the triaxiality of the bigger primary in the framework of the relativistic R3BP. It is observed that the locations of these points are affected by the relativistic factor, triaxiality and a small perturbation in the centrifugal force, but are unaffected by that of the Coriolis force. It is also seen that for these points the range of stability region increases or decreases according as equation (14) without is greater or less than zero.

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