Stability Of Triangular Equilibrium Points Research Articles

Effects of zonal harmonics and a circular cluster of material points on the stability of triangular equilibrium points in the R3BP

We have studied a modified version of the classical restricted three-body problem (CR3BP) where both primaries are considered as oblate spheroids and are surrounded by a homogeneous circular planar cluster of material points centered at the mass center of the system. In this dynamical model we have examined the effects of oblateness of both primaries up to zonal harmonic J 4; together with gravitational potential from the circular cluster of material points on the existence and linear stability of the triangular equilibrium points. It is found that, the triangular points are stable for 0<μ<μ c and unstable for $\mu_{c} \le \mu \le \frac{1}{2}$ , where μ c is the critical mass ratio affected by the oblateness up to J 4 of the primaries and potential from the circular cluster of material points. The coefficient J 4 has stabilizing tendency, while J 2 and the potential from the circular cluster of material points have destabilizing tendency. A practical application of this model could be the study of the motion of a dust particle near oblate bodies surrounded by a circular cluster of material points.

Effects of radiation on stability of triangular equilibrium points in elliptic restricted three body problem

This paper deals with the stability of triangular Lagrangian points in the elliptical restricted three body problem, under the effect of radiation pressure stemming from the more massive primary on the infinitesimal. We adopted a set of rotating pulsating axes centered at the centre of mass of the two primaries Sun and Jupiter. We have exploited method of averaging used by Grebenikov, throughout the analysis of stability of the system. The critical mass ratio depends on the radiation pressure, eccentricity and the range of stability decreases as the radiation parameter increases. Keywords: Dynamical system, elliptical restricted three body problems, lagrangian points, radiation pressure, and stability.

On the stability of triangular points in the elliptic R3BP under radiating and oblate primaries

This paper investigates the stability of triangular equilibrium points (L4,5) in the elliptic restricted three-body problem (ER3BP), when both oblate primaries emit light energy simultaneously. The positions of the triangular points are seen to shift away from the line joining the primaries than in the classical case on account of the introduction of the eccentricity, semi-major axis, radiation and oblateness factors of both primaries. This is shown for the binary systems Achird, Luyten 726-8, Kruger 60, Alpha Centauri AB and Xi Bootis. We found that motion around these points is conditionally stable with respect to the parameters involved in the system dynamics. The region of stability increases and decreases with variability in eccentricity, oblateness and radiation pressures.

Nonlinear stability in the generalised photogravitational restricted three body problem with Poynting-Robertson drag

The nonlinear stability of triangular equilibrium points has been discussed in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. We have performed first and second order normalization of the Hamiltonian of the problem. We have applied KAM theorem to examine the condition of non-linear stability. We have found three critical mass ratios. Finally we conclude that triangular points are stable in the nonlinear sense except three critical mass ratios at which KAM theorem fails.

Linear Stability of Triangular Equilibrium Points in the Photogravitational Restricted Three Body Problem with Poynting -Robertson Drag when both Primaries are Oblate Spheroid

We have examined the linear stability of triangular equilibrium points in the photogravitational restricted three body problem with Poynting- Robertson drag when both primaries are considered as radiating as well as oblate spheroid. We have found the position of triangular equilibrium points of our problem. The equations of motion are affected by radiation pressure force, oblateness and P-R drag. With the help of characteristic equation, we have discussed the stability conditions. All classical results involving photogravitational and oblateness in restricted three body problem may be verified from this result.

Nonlinear Stability in Generalized Photogravitational Restricted Three Body Problem

We have discussed the nonlinear stability of triangular equilibrium points in generalized photogravitational restricted three body problem. The problem is generalized in the sense that both primaries are taken as oblate spheroid. We have performed first and second normalization of the Hamiltonian of the problem We have applied Arnold’s theorem to examine the condition of non-linear stability. We have found three critical mass ratios where this theorem fails. The stability condition is different from the classical case due to radiation and oblateness of the primaries.

Linear Stability of Triangular Equilibrium Points in the Generalized Photogravitational Restricted Three Body Problem with Poynting_Robertson Drag

In this paper we have examined the linear stability of triangular equilibrium points in the generalised photogravitational restricted three body problem with Poynting-Robertson drag. We have found the position of triangular equilibrium points of our problem. The problem is generalised in the sense that smaller primary is supposed to be an oblate spheroid. The bigger primary is considered as radiating. The equations of motion are affected by radiation pressure force, oblateness and P-R drag. All classical results involving photogravitational and oblateness in restricted three body problem may be verified from this result. With the help of characteristic equation, we discussed the stability. Finally we conclude that triangular equilibrium points are unstable.