scholarly journals Some remarks on the stability analysis in Robe's three body problem

1982 ◽  
Vol 5 (1) ◽  
pp. 195-202
Author(s):  
R. Meire
Keyword(s):  
Stability Analysis ◽  
Differential Equations ◽  
Body Problem ◽  
Computer Time ◽  
System Of Differential Equations ◽  
Three Body Problem ◽  
The Stability ◽  
Three Body ◽  
Improved Technique ◽  
Transition Curves

An improved technique is presented for the stability analysis of Robe's3-body problem which gives more accurate results for the transition curves in the parameter plane than does Robe's paper.A novel property of the system of differential equations describing the motion is used, which reduces the computer time by more than50%.

scholarly journals Characteristics exponents of the triangular solution in the elliptical restricted three-body problem under radiating and triaxial primaries

2017 ◽  
Vol 5 (1) ◽  
pp. 12 ◽  
Author(s):  
Ashutosh Narayan ◽  
Krishna Kumar Pandey ◽  
Sandip Kumar Shrivastava
Keyword(s):  
Analytical Method ◽  
Body Problem ◽  
Equilibrium Points ◽  
Periodic Coefficient ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Characteristic Exponents ◽  
The Stability ◽  
Three Body ◽  
Transition Curves

This Paper deals with the effects of the radiation pressure and triaxiality of primaries on the stability of infinitesimal motion about triangular equilibrium points [ , ] in the elliptical restricted three body problem (ER3EB) around binary system. For determining the characteristic exponents of variational equations with periodic coefficient, we have used analytical method, described by Bennet in [3, 4]. This analytical method is based on Floquet’s theory. The stability of equilibrium points has been discussed under the assumption thatboth the primaries are radiating and triaxial. For this we have drawn transition cureves in μ-e plane. And it is seen that system is stable outside the transition curves, while system is Unstable within the transition curves.

scholarly journals On the Stability of Collinear Points of the RTBP with Triaxial and Oblate Primaries and Relativistic Effects

2021 ◽  
pp. 56-73
Author(s):  
S. E. Abd El-Bar
Keyword(s):  
Characteristic Equation ◽  
Body Problem ◽  
Equilibrium Points ◽  
Equations Of Motion ◽  
Relativistic Effects ◽  
Three Body Problem ◽  
Total Potential ◽  
The Mean ◽  
The Stability ◽  
Three Body

Under the influence of some different perturbations, we study the stability of collinear equilibrium points of the Restricted Three Body Problem. More precisely, the perturbations due to the triaxiality of the bigger primary and the oblateness of the smaller primary, in addition to the relativistic effects, are considered. Moreover, the total potential and the mean motion of the problem are obtained. The equations of motion are derived and linearized around the collinear points. For studying the stability of these points, the characteristic equation and its partial derivatives are derived. Two real and two imaginary roots of the characteristic equation are deduced from the plotted figures throughout the manuscript. In addition, the instability of the collinear points is stressed. Finally, we compute some selected roots corresponding to the eigenvalues which are based on some selected values of the perturbing parameters in the Tables 1, 2.

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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