scholarly journals Linear Stability of the Elliptic Lagrangian Triangle Solutions in the Three-Body Problem

2002 ◽  
Vol 182 (1) ◽  
pp. 191-218 ◽  
Author(s):  
Gareth E. Roberts
Keyword(s):  
Linear Stability ◽  
Body Problem ◽  
Three Body Problem ◽  
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.

ω-Index Theory and Linear Stability of Elliptic Lagrangian Solutions of the Classical Three-Body Problem

2012 ◽  
Vol 12 (4) ◽  
Author(s):  
Yiming Long
Keyword(s):  
Linear Stability ◽  
Equilateral Triangle ◽  
Body Problem ◽  
Mass Parameter ◽  
Index Theory ◽  
Three Body Problem ◽  
Homographic Solutions ◽  
Three Body

AbstractIt is well known that the linear stability of Lagrangian elliptic equilateral triangle homographic solutions in the classical planar three-body problem depends on the mass parameter β = 27(m

scholarly journals On stability of triangular points of the restricted relativistic elliptic three-body problem with triaxial and oblate primaries

2017 ◽  
pp. 47-52
Author(s):  
K. Zahra ◽  
Z. Awad ◽  
H.R. Dwidar ◽  
M. Radwan
Keyword(s):  
Linear Stability ◽  
Body Problem ◽  
Critical Mass ◽  
Combined Effects ◽  
Mass Ratio ◽  
Three Body Problem ◽  
Triangular Points ◽  
The Stability ◽  
Three Body ◽  
Ratio Range

This paper investigates the location and linear stability of triangular points under combined effects of perturbations: triaxialty of a massive primary, oblateness of a less massive one, and relativistic corrections. The primaries in this system are assumed to move in elliptical orbits around their common barycenter. It is found that the locations of the triangular points are affected by the involved perturbations. The stability of orbits near these points is also examined. We observed that these points are stable for the mass ratio, ?, range 0 < ? < ?c, where ?c is the critical mass ratio, and unstable for the range ?c ? ? ? 0.5.

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