scholarly journals Robe's Restricted Three-Body Problem with Variable Masses and Perturbing Forces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Jagadish Singh ◽  
Oni Leke
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Second Primary ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Small Perturbations ◽  
Triangular Points ◽  
Numerical Exploration ◽  
Three Body ◽  
Infinitesimal Mass

The linear stability of equilibrium points of a test particle of infinitesimal mass in the framework of Robe's circular restricted three-body problem, as in Hallan and Rana, together with effect of variation in masses of the primaries with time according to the combined Meshcherskii law, is investigated. It is seen that, due to a small perturbation in the centrifugal force and an arbitrary constant of a particular integral of the Gylden-Meshcherskii problem, every point on the line joining the centers of the primaries is an equilibrium point provided they lie within the shell. Further, a number of pairs of equilibrium points lying on the -plane and forming triangles with the centers of the shell and the second primary exist, for some values of . The points collinear with the center of the shell are found to be stable under some conditions and the range of stability depends on the small perturbations and , while the triangular points are unstable. Illustrative numerical exploration is given to indicate significant improvement of the problem in Hallan and Rana.

scholarly journals Pulsating curves of zero velocity for infinitesimal mass around oblate and triaxial rigid body of triangular equilibrium points in elliptical restricted three body problem

2017 ◽  
Vol 5 (1) ◽  
pp. 29
Author(s):  
Nutan Singh ◽  
A. Narayan
Keyword(s):  
Rigid Body ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Triaxial Rigid Body ◽  
Three Body ◽  
Infinitesimal Mass

This paper explore pulsating Curves of zero velocityof the infinitesimal mass around the triangular equilibrium points with oblate and triaxial rigid body in the elliptical restricted three body problem(ER3BP).

scholarly journals Pulsating Different Curves of Zero Velocity around Triangular Equilibrium Points in Elliptical Restricted Three-Body Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
A. Narayan ◽  
Amit Shrivastava
Keyword(s):  
Binary Systems ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Triangular Points ◽  
Zero Velocity ◽  
Simulation Techniques ◽  
The Stability ◽  
Three Body

The oblateness and the photogravitational effects of both the primaries on the location and the stability of the triangular equilibrium points in the elliptical restricted three-body problem have been discussed. The stability of the triangular points under the photogravitational and oblateness effects of both the primaries around the binary systems Achird, Lyeten, Alpha Cen-AB, Kruger 60, and Xi-Bootis, has been studied using simulation techniques by drawing different curves of zero velocity.

Motion around the Triangular Equilibrium Points in the Circular Restricted Three-Body Problem under Triaxial Luminous Primaries with Poynting-Robertson Drag

2017 ◽  
Vol 12 ◽  
pp. 1-21
Author(s):  
Jagadish Singh ◽  
Ayas Mungu Simeon
Keyword(s):  
Linear Stability ◽  
Binary Stars ◽  
Body Problem ◽  
Equilibrium Points ◽  
Rigid Bodies ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Numerical Application ◽  
Triangular Points ◽  
Three Body

This paper explores the motion of an infinitesimal body around the triangular equilibrium points in the framework of circular restricted three-body problem (CR3BP) with the postulation that the primaries are triaxial rigid bodies, radiating in nature and are also under the influence of Poynting–Robertson (P-R) drag. We study the linear stability of these triangular points and for the numerical application, the binary stars Kruger 60 (AB) and Archird have been considered. These triangular points are not only perceived to move towards the line joining the primaries in the direction of the bigger primary with increasing triaxiality, they are also unstable owing to the destabilizing influence of P-R drag.

scholarly journals Influence of the Zonal Harmonics of the Primary on L4,5 in the Photogravitational ER3BP

2016 ◽  
Vol 10 ◽  
pp. 23-36
Author(s):  
Jagadish Singh ◽  
Blessing Ashagwu ◽  
Aishetu Umar
Keyword(s):  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Systems Dynamics ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Triangular Points ◽  
Zonal Harmonics ◽  
Three Body

We investigate in the framework of the elliptic restricted three-body problem (ER3BP), the influence of the zonal harmonics (J2and J4) of the primary and the radiation pressure of the secondary on the positions and stability of the triangular equilibrium points. The triangular points of the problem are affected by the parameters involved in the systems’ dynamics. The positions change with increase in the zonal harmonics, eccentricity and radiation pressure. The triangular points remain stable in the interval 0<μ<μcas shown arbitrarily.

scholarly journals On Motion around the Collinear Equilibrium Points in the Relativistic R3BP with a Smaller Triaxial Primary

2018 ◽  
Vol 13 ◽  
pp. 1-11
Author(s):  
Bello Nakone ◽  
Jagadish Singh
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
The Sun ◽  
Three Body Problem ◽  
Numerical Studies ◽  
Three Body ◽  
Infinitesimal Mass

This paper studies the motion of an infinitesimal mass near the collinear equilibrium points in the framework of relativistic restricted three-body problem (R3BP) when the smaller primary is a triaxial body. It is observed that the positions of the collinear points are affected by the relativistic and triaxiality factors. The collinear points are found to remain unstable. Numerical studies in this connection, with the Sun-Earth, Sun-Pluto and Earth-Moon systems have been carried out to show the relativistic and triaxiality effects.

scholarly journals Effects of Perturbations on the Stability of Equilibrium Points in the CR3BP with Luminous and Heterogeneous Spheroid Primaries

2021 ◽  
Author(s):  
Jagadish Singh ◽  
Shitu Muktar Ahmad
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Critical Mass ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Triangular Points ◽  
Stability Of Equilibrium ◽  
Oblate Spheroids ◽  
The Stability ◽  
Three Body

Abstract This paper studies the position and stability of equilibrium points in the circular restricted three-body problem (CR3BP) under the influence of small perturbations in the Coriolis and centrifugal forces when the primaries are radiating and heterogeneous oblate spheroids. It is seen that there exist five libration points as in the classical restricted three-body problem, three collinear Li(i=1,2,3) and two triangular Li(i= 4,5). It is also seen that the triangular points are no longer to form equilateral triangles with the primaries rather they form simple triangles with line joining the primaries. It is further observed that despite all perturbations the collinear points remain unstable while the triangular points are stable for 0 < µ < µc and unstable for µc ≤ µ ≤ ½, where µc is the critical mass ratio depending upon aforementioned parameters. It is marked that small perturbation in the Coriolis force, radiation and heterogeneous oblateness of the both primaries have destabilizing tendencies. Their numerical examination is also performed.

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.

scholarly journals LOCATION AND STABILITY OF THE TRIANGULAR POINTS IN THE TRIAXIAL ELLIPTIC RESTRICTED THREE-BODY PROBLEM

2021 ◽  
Vol 57 (2) ◽  
pp. 311-319
Author(s):  
M. Radwan ◽  
Nihad S. Abd El Motelp
Keyword(s):  
Linear Stability ◽  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stability Regions ◽  
Triangular Points ◽  
Problem Frame ◽  
The Stability ◽  
Three Body

The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is generalized in the sense that the two primaries are considered as triaxial bodies. It was found that the locations of these points are affected by the triaxiality coefficients of the primaries and the eccentricity of orbits. Also, the stability regions depend on the involved perturbations. We also studied the periodic orbits in the vicinity of the triangular points.

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