scholarly journals Qualitative Analysis of Some Libration Points in the Restricted Four-body Problem

2021 ◽  
Vol 17 (4) ◽  
pp. 369-390
Author(s):  
A. Ligȩza ◽  
◽  
H. Żoła̧dek ◽  
Keyword(s):  
Qualitative Analysis ◽  
Linear Approximation ◽  
Lyapunov Stability ◽  
Body Problem ◽  
Kam Theory ◽  
Libration Points ◽  
Fixed Plane ◽  
Four Body Problem

We consider the situation where three heavy gravitational bodies form the Lagrange configuration rotating in a fixed plane and the fourth body of negligible mass moves in this plane. We present three cases of so-called libration points and we study their stability using linear approximation and KAM theory. In some situations we prove the Lyapunov stability for generic values of some parameter of the problem.

On the existence of libration points in the spatial collinear restricted four-body problem within frame of repulsive Manev potential and variable mass

2018 ◽  
Vol 117 ◽  
pp. 94-104 ◽  
Author(s):  
Md Sanam Suraj ◽  
Amit Mittal ◽  
Charanpreet Kaur ◽  
Rajiv Aggarwal
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Libration Points ◽  
Four Body Problem

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.

scholarly journals Equilibrium Points and Basins of Convergence in the Triangular Restricted Four-Body Problem with a Radiating Body

2020 ◽  
Vol 30 (02) ◽  
pp. 2030003 ◽  
Author(s):  
J. E. Osorio-Vargas ◽  
Guillermo A. González ◽  
F. L. Dubeibe
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Center Of Mass ◽  
Libration Points ◽  
The Sun ◽  
Radiation Factor ◽  
Trojan Asteroid ◽  
Four Body Problem ◽  
Common Center ◽  
The Stability

In this paper, we extend the basic equilateral four-body problem by introducing the effect of radiation pressure, Poynting–Robertson drag, and solar wind drag. In our setup, three primaries lie at the vertices of an equilateral triangle and move in circular orbits around their common center of mass. Here, one of the primaries is a radiating body and the fourth body (whose mass is negligible) does not affect the motion of the primaries. We show that the existence and the number of equilibrium points of the problem depend on the mass parameters and radiation factor. Consequently, the allowed regions of motion, the regions of the basins of convergence for the equilibrium points, and the basin entropy will also depend on these parameters. The present dynamical model is analyzed for three combinations of mass for the primaries: equal masses, two equal masses, different masses. As the main results, we find that in all cases the libration points are unstable if the radiation factor is larger than 0.01 and hence able to destroy the stability of the libration points in the restricted four-body problem composed by the Sun, Jupiter, Trojan asteroid and a test (dust) particle. Also, we conclude that the number of fixed points decreases with the increase of the radiation factor.

Restricted four-body problem. The case of a central configuration: Libration points and their stability

2008 ◽  
Vol 34 (5) ◽  
pp. 357-365 ◽  
Author(s):  
Yu. D. Medvedev ◽  
N. I. Perov
Keyword(s):  
Body Problem ◽  
Libration Points ◽  
Central Configuration ◽  
Four Body Problem

scholarly journals STABILITY ABOUT LIBRATION POINTS FOR RESTRICTED FOUR-BODY PROBLEM

2019 ◽  
Vol 30 (2) ◽  
pp. 1-11
Author(s):  
M. Ismail ◽  
A. Ibrahim ◽  
A. Zaghrout ◽  
S. Younis ◽  
F. Elmalky ◽  
...  
Keyword(s):  
Body Problem ◽  
Libration Points ◽  
Four Body Problem

scholarly journals On the Lagrange libration points of the perturbed Earth-Moon System

2014 ◽  
Vol 9 (S310) ◽  
pp. 192-193 ◽  
Author(s):  
Tatiana V. Salnikova ◽  
Sergey Ya. Stepanov
Keyword(s):  
Body Problem ◽  
Libration Points ◽  
Moon System ◽  
The Earth ◽  
Four Body Problem

AbstractIn this work we discuss the elusive Kordylewski clouds – dust matter in the neighborhood of the Lagrange libration points L4, L5 of the Earth-Moon system. On the base of restricted planar circular four body problem we get some proof for possibility of existence of four such clouds and some rule to predict the optimal moments of time for their observation.

Stability of libration points in the restricted four-body problem with variable mass

2016 ◽  
Vol 361 (10) ◽  
Author(s):  
Amit Mittal ◽  
Rajiv Aggarwal ◽  
Md. Sanam Suraj ◽  
Virender Singh Bisht
Keyword(s):  
Body Problem ◽  
Variable Mass ◽  
Libration Points ◽  
Four Body Problem
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