Stability of equilibrium points in the generalized perturbed restricted three-body problem

Abstract

This paper studies the existence and stability of equilibrium points under the influence of small perturbations in the Coriolis and the centrifugal forces, together with the non-sphericity of the primaries. The problem is generalized in the sense that the bigger and smaller primaries are respectively triaxial and oblate spheroidal bodies. It is found that the locations of equilibrium points are affected by the non-sphericity of the bodies and the change in the centrifugal force. It is also seen that the triangular points are stable for 0 < μ < μ c and unstable for μ c ≤ μ < 1 2 , where μ c is the critical mass parameter depending on the above perturbations, triaxiality and oblateness. It is further observed that collinear points remain unstable.

The Collinear Libration Points in the Elliptic R3BP with a Triaxial Primary and an Oblate Secondary

“…They are seen to be affected by the shape of the participating bodies and their orbital geometries. These results agree with [27] in the absence of oblateness and with [37] in the circular case. The collinear points also remain unstable due to the presence of real roots and despite the introduction of the triaxiality and oblateness parameters.…”

Periodic Orbits around Triangular Points in the Restricted Problem of Three Oblate Bodies

“…In the second coefficient of (10), the term containing a small change in the centrifugal in AbdulRaheem and Singh [2] are different while the other terms are same with ours. In Singh and Begha [18], the all the terms there are a found in ours when 2 1 σ σ = . In the third coefficient, our results are in accordance with that in AbdulRaheem and Singh [2] but again the term containing the small change, differs.…”

“…We note that the first coefficient in the equation are same with that in AbdulRaheem and Singh [2], except for what seems like a typographic error in the coefficient of the oblateness of the bigger primary. However, the coefficients of the term containing triaxiality of the bigger primary in the paper by Singh and Begha [18] are equally erroneous. In the second coefficient of (10), the term containing a small change in the centrifugal in AbdulRaheem and Singh [2] are different while the other terms are same with ours.…”

“…The combine effect of radiation, perturbations and oblateness on the periodic orbits was carried out by AbdulRaheem and Singh [2]. Singh and Begha [18] looked at the problem of the periodic orbits when the larger and smaller primaries are triaxial and oblate bodies respectively under effects of small perturbations in the Coriolis and centrifugal forces. Perdiou et al [7] studied the periodic motions in the spatial Chermnykh's restricted three-body problem.…”

Existence and linear stability of triangular points in the perturbed relativistic R3BP when the bigger primary is an oblate spheroid

“…The stability is actually achieved through the influence of the Coriolis force, because the coordinate system is rotating (Wintner [2]; Contopolous [3]). Various contributions (Szebehely [4]; Bhatnagar and Hallan [5]; AbdulRaheem and Singh [6]; Singh and Begha [7]; and Abouelmagd et al [8]) have been made on the study of the restricted three-body problem under the effects of small perturbations in the centrifugal and Coriolis forces. Szebehely [4] investigated the stability of triangular points by keeping the centrifugal force constant and found that the Coriolis force is a stabilizing force.…”