scholarly journals The orbital stability of a test body motion in the field of two massive bodies

2018 ◽  
Vol 168 ◽  
pp. 04001
Author(s):  
Medeu Abishev ◽  
Saken Toktarbay ◽  
Aigerim Abylayeva ◽  
Amanhan Talkhat
Keyword(s):  
Body Problem ◽  
Orbital Stability ◽  
Test Body ◽  
Body Motion ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Test Particles ◽  
The Stability ◽  
Three Body ◽  
Insight Into

We investigate the orbital stability of a test particle motion in the restricted three-body problem where all bodies have their own rotation. We have shown that it is possible to get some insight into the stability properties of the motion of test particles in restricted three-body problem, without knowing the exact solutions of the relativistic motion equations.

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 Orbital stability of high inclination asteroids

1996 ◽  
Vol 172 ◽  
pp. 187-192
Author(s):  
N. A. Solovaya ◽  
E. M. Pittich
Keyword(s):  
Solar System ◽  
Body Problem ◽  
Equations Of Motion ◽  
Orbital Stability ◽  
Dynamical Model ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

The orbital evolutions of fictitious asteroids with high inclinations have been investigated. The selected initial orbits represent asteroids with movement, which corresponds to the conditions of the Tisserand invariant for C = C (L1) in the restricted three body problem. Initial eccentricities of the orbits cover the interval 0.0–0.4, inclinations the interval 40–80°, and arguments of perihelion the interval 0–360°. The equations of motion of the asteroids were numerically integrated from the epoch March 25, 1991 forward within the interval of 20,000 years, using a dynamical model of the solar system consisting of all planets. The orbits of the model asteroids are stable at least during the investigated period.

scholarly journals Quasi-Lntegrals of the Plane Restricted Three-Body Problem

1993 ◽  
Vol 132 ◽  
pp. 309-319
Author(s):  
E.M. Nezhinskij
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Test Body ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Jacobi Integral ◽  
Three Body ◽  
Two Bodies

AbstractThe paper is concerned with studying the domain of possible motion and a field of the test body velocities in the plane restricted problem of three bodies. The study is based on existence of a quasi-integral of areas (similar to an integral of areas in the problem of two bodies) as well as on the Jacobi integral. The method of constructing the quasi-integrals is a standard one (see, for example, [1],[2].

scholarly journals Stability of the Sitnikov's circular restricted three body problem when the primaries are oblate spheroid

BIBECHANA ◽  
2014 ◽  
Vol 11 ◽  
pp. 149-156
Author(s):  
RR Thapa
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Oblate Spheroid ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Third Body ◽  
Independent Variable ◽  
The Stability ◽  
Three Body ◽  
Special Case

The Sitnikov's problem is a special case of restricted three body problem if the primaries are of equal masses (m1 = m2 = 1/2) moving in circular orbits under Newtonian force of attraction and the third body of mass m3 moves along the line perpendicular to plane of motion of primaries. Here oblate spheroid primaries are taken. The solution of the Sitnikov's circular restricted three body problem has been checked when the primaries are oblate spheroid. We observed that solution is depended on oblate parameter A of the primaries and independent variable τ = ηt. For this the stability of non-trivial solutions with the characteristic equation is studied. The general equation of motion of the infinitesimal mass under mutual gravitational field of two oblate primaries are seen at equilibrium points. Then the stability of infinitesimal third body m3 has been calculated. DOI: http://dx.doi.org/10.3126/bibechana.v11i0.10395 BIBECHANA 11(1) (2014) 149-156

scholarly journals Investigation of the Stability of a Test Particle in the Vicinity of Collinear Points with the Additional Influence of an Oblate Primary and a Triaxial-Stellar Companion in the Frame of ER3BP

2018 ◽  
Vol 13 ◽  
pp. 12-27 ◽  
Author(s):  
Aminu Abubakar Hussain ◽  
Aishetu Umar ◽  
Jagadish Singh
Keyword(s):  
Numerical Analysis ◽  
Body Problem ◽  
Major Axis ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Semi Major Axis ◽  
Primary Body ◽  
Additional Influence ◽  
The Stability ◽  
Three Body

We investigate in the elliptic framework of the restricted three-body problem, the motion around the collinear points of an infinitesimal particle in the vicinity of an oblate primary and a triaxial stellar companion. The locations of the collinear points are affected by the eccentricity of the orbits, oblateness of the primary body and the triaxiality and luminosity of the secondary. A numerical analysis of the effects of the parameters on the positions of collinear points of CEN X-4 and PSR J1903+0327 reveals a general shift away from the smaller primary with increase in eccentricity and triaxiality factors and a shift towards the smaller primary with increase in the semi-major axis and oblateness of the primary on L1. The collinear points remain unstable in spite of the introduction of these parameters.

scholarly journals Study of the stability of the perturbed solutions of the restricted three body problem

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 18-22
Author(s):  
MAA Khan ◽  
MR Hassan ◽  
RR Thapa
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Variational Equations ◽  
First Order ◽  
Characteristic Exponents ◽  
Method Of Determination ◽  
The Stability ◽  
Three Body

In this paper we have been examined the stability of the perturbed solutions of the restricted three body problem. We have been restricted ourselves only to the first order variational equations. Our variational equations depend on the periodic solutions. Here the applications of the method of Fuchs and Floquet Proves to be complicated and hence we have been preferred Poincare's Method of determination of the characteristic exponents. With the determination of the characteristic exponents we have been abled to conclude regarding the stability of the generating solution. We have obtained that the motions are unstable in all the cases. By Poincare's implicit function theorem we have concluded that the stability would remain the same for small value of the parameter m and in all types of motion of the restricted three-body problem.BIBECHANA 13 (2016) 18-22 

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