On the practical stability of the triangular points in the restricted three-body problem

1971 ◽  
Vol 4 (1) ◽  
pp. 3-14
Author(s):  
Jacek Olszewski
Keyword(s):  
Body Problem ◽  
Practical Stability ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Triangular Points ◽  
Three Body

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.

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

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.

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.

Sign in / Sign up

Export Citation Format

Share Document