Effect of perturbations in coriolis and centrifugal forces on the location and stability of the equilibrium point in the Robe's circular restricted three body problem

2001 ◽  
Vol 49 (9) ◽  
pp. 957-960 ◽  
Author(s):  
P.P. Hallan ◽  
Neelam Rana
Keyword(s):  
Equilibrium Point ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Centrifugal Forces ◽  
Three Body Problem ◽  
Coriolis And Centrifugal Forces ◽  
Three Body

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 Diagonalization of Hamiltonian in the photogravitation-al restricted three body problem with P-R drag

2017 ◽  
Vol 5 (2) ◽  
pp. 79 ◽  
Author(s):  
Xavier James Raj ◽  
Bhola Ishwar
Keyword(s):  
Power Series ◽  
Equilibrium Point ◽  
Body Problem ◽  
Equilibrium Points ◽  
Lagrangian Function ◽  
Quadratic Term ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body ◽  
Taylor’S Series

In this paper, restricted, three-body problem (RTBP) is generalised to study the non-linear stability of equilibrium points in the photogravitational RTBP with P-R drag. In the present study, both primaries are considered as a source of radiation and effect of P-R drag. Hence the problem will contain four parameters q1, q2, W1 and W2. At first, the Lagrangian and the Hamiltonian of the problem were computed, then the Lagrangian function is expanded in power series of the coordinates of the triangular equilibrium points x and y. Lastly, diagonalized the quadratic term of the Hamiltonian of the problem, which is obtained by expanding original Lagrangian or Hamiltonian by Taylor's series about triangular equilibrium point. Finally, the study concluded that the diagonalizable Hamiltonian is H2=ω1I1-ω2I2.

scholarly journals Existence and Linear Stability of Equilibrium Points in the Robe’s Restricted Three-Body Problem with Oblateness

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Jagadish Singh ◽  
Abubakar Umar Sandah
Keyword(s):  
Equilibrium Point ◽  
Linear Stability ◽  
Body Problem ◽  
Equilibrium Points ◽  
Oblate Spheroid ◽  
Second Primary ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Out Of Plane ◽  
Three Body

This paper investigates the positions and linear stability of an infinitesimal body around the equilibrium points in the framework of the Robe’s circular restricted three-body problem, with assumptions that the hydrostatic equilibrium figure of the first primary is an oblate spheroid and the second primary is an oblate body as well. It is found that equilibrium point exists near the centre of the first primary. Further, there can be one more equilibrium point on the line joining the centers of both primaries. Points on the circle within the first primary are also equilibrium points under certain conditions and the existence of two out-of-plane points is also observed. The linear stability of this configuration is examined and it is found that points near the center of the first primary are conditionally stable, while the circular and out of plane equilibrium points are unstable.

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