On the Nature of Equilibrium Points in the Axisymmetric Five-Body Problem

2021 ◽  
Author(s):  
Shah Muhammad ◽  
Faisal Duraihem ◽  
Wei Chen ◽  
Euaggelos Zotos
Keyword(s):  
Numerical Methods ◽  
Linear Stability ◽  
Body Problem ◽  
Equilibrium Points ◽  
Central Configurations ◽  
Rigorous Analysis ◽  
Stable Equilibria ◽  
Specific Configuration

Abstract The aim of this work is to numerically investigate the nature of the equilibrium points of the axisymmetric five-body problem. Specifically, we consider two cases regarding the convex or concave configuration of the four primary bodies. The specific configuration of the primaries depends on two angle parameters. Combining numerical methods with systematic and rigorous analysis, we reveal how the angle parameters affect not only the relative positions of the equilibrium points but also their linear stability. Our computations reveal that linearly stable equilibria exist in all possible central configurations of the primaries, thus improving and also correcting the findings of previous similar works.

Exploring the Location and Linear Stability of the Equilibrium Points in the Equilateral Restricted Four-Body Problem

2020 ◽  
Vol 30 (10) ◽  
pp. 2050155
Author(s):  
Euaggelos E. Zotos
Keyword(s):  
Linear Stability ◽  
Body Problem ◽  
Equilibrium Points ◽  
Libration Points ◽  
The Other ◽  
Classification Method ◽  
Four Body Problem ◽  
The Masses ◽  
Stable Points ◽  
Planar Version

The planar version of the equilateral restricted four-body problem, with three unequal masses, is numerically investigated. By adopting the grid classification method we locate the coordinates, on the plane [Formula: see text], of the points of equilibrium, for all possible values of the masses of the primaries. The linear stability of the libration points is also determined, as a function of the masses. Our analysis indicates that linearly stable points of equilibrium exist only when one of the primaries has a considerably larger mass, with respect to the other two primary bodies, when the triangular configuration of the primaries is also dynamically stable.

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 Effects of the albedo and disc on the zero velocity curves and linear stability of equilibrium points in the generalized restricted three-body problem

2019 ◽  
Vol 488 (2) ◽  
pp. 1894-1907
Author(s):  
Saleem Yousuf ◽  
Ram Kishor
Keyword(s):  
Linear Stability ◽  
Radiation Pressure ◽  
Body Problem ◽  
Equilibrium Points ◽  
Mass Parameter ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Zero Velocity Curves ◽  
Three Body

ABSTRACT The important aspects of a dynamical system are its stability and the factors that affect its stability. In this paper, we present an analysis of the effects of the albedo and the disc on the zero velocity curves, the existence of equilibrium points and their linear stability in a generalized restricted three-body problem (RTBP). The proposed problem consists of the motion of an infinitesimal mass under the gravitational field of a radiating-oblate primary, an oblate secondary and a disc that is rotating about the common centre of mass of the system. Significant effects of the albedo and the disc are observed on the zero velocity curves, on the positions of equilibrium points and on the stability region. A linear stability analysis of collinear equilibrium points L1, 2, 3 is performed with respect to the mass parameter μ and albedo parameter QA of the secondary, separately. It is found that L1, 2, 3 are unstable in both cases. However, the non-collinear equilibrium points L4, 5 are stable in a finite range of mass ratio μ. After analysing the individual as well as combined effects of the radiation pressure force of the primary, the albedo force of the secondary, the oblateness of both the primary and secondary and the disc, it is found that these perturbations play a significant role in the design of the trajectories in the vicinity of equilibrium points and in the analysis of their stability property. In the future, the results obtained will improve existing results and will help in the analysis of different space missions. These results are limited to the regular symmetric disc and radiation pressure, which can be extended later.

scholarly journals Perturbed locations and linear stability of collinear Lagrangian points in the elliptic restricted three body problem with triaxial primaries

2019 ◽  
Vol 28 (1) ◽  
pp. 145-153
Author(s):  
Walid Ali Rahoma ◽  
Akram Masoud ◽  
Fawzy Ahmed Abd El-Salam ◽  
Elamira Hend Khattab
Keyword(s):  
Linear Stability ◽  
Body Problem ◽  
Equilibrium Points ◽  
Classical Case ◽  
Restricted Three Body Problem ◽  
Mass Ratio ◽  
Three Body Problem ◽  
The Difference ◽  
The Stability ◽  
Three Body

Abstract This paper aims to study the effect of the triaxiality and the oblateness as a special case of primaries on the locations and stability of the collinear equilibrium points of the elliptic restricted three body problem (in brief ERTBP). The locations of the perturbed collinear equilibrium points are first determined in terms of mass ratio of the problem (the smallest mass divided by the total mass of the system) and different concerned perturbing factors. The difference between the locations of collinear points in the classical case of circular restricted three body problem and those in the perturbed case is represented versus mass ratio over its range. The linear stability of the collinear points is discussed. It is observed that the stability regions for our model depend mainly on the eccentricity of the orbits in addition to the considered perturbations.

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