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 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 Nekhoroshev-Stability ofL4andL5in the Spatial Restricted Problem

1999 ◽  
Vol 172 ◽  
pp. 445-446 ◽  
Author(s):  
Giancarlo Benettin ◽  
Francesco Fassò ◽  
Massimiliano Guzzo
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Critical Mass ◽  
Kam Theory ◽  
Birkhoff Normal Form ◽  
Three Body Problem ◽  
Arnold Diffusion ◽  
Convexity Assumption ◽  
Three Body ◽  
Nekhoroshev Stability

The Lagrangian equilateral pointsL4andL5of the restricted circular three-body problem are elliptic for all values of the reduced massμbelow Routh’s critical massμR≈ .0385. In the spatial case, because of the possibility of Arnold diffusion, KAM theory does not provide Lyapunov-stability. Nevertheless, one can consider the so-called ‘Nekhoroshev-stability’: denoting byda convenient distance from the equilibrium point, one asks whetherfor any small єe > 0, with positiveaandb. Until recently this problem, as more generally the problem of Nekhoroshev-stability of elliptic equilibria of Hamiltonian systems, was studied only under some arithmetic conditions on the frequencies, and thus onμ(see e.g .Giorgilli, 1989). Our aim was instead considering all values ofμup toμR. As a matter of fact, Nekhoroshev-stability of elliptic equilibria, without any arithmetic assumption on the frequencies, was proved recently under the hypothesis that the fourth order Birkhoff normal form of the Hamiltonian exists and satisfies a ‘quasi-convexity’ assumption (Fassòet al, 1998; Guzzoet al, 1998; Niedermann, 1998).

scholarly journals On the Nonlinear Stability of the Triangular Points in the Circular Spatial Restricted Three-body Problem

2020 ◽  
Vol 25 (2) ◽  
pp. 131-148
Author(s):  
Daniela Cárcamo-Díaz ◽  
Jesús F. Palacián ◽  
Claudio Vidal ◽  
Patricia Yanguas
Keyword(s):  
Nonlinear Stability ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Triangular Points ◽  
Three Body
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