“…Furthermore, the nonlinear stability of the infinitesimal in the orbits or the size of the stable region around L 4 was "studied by Gyorgrey [16]" and the parametric resonance stability around L 4, in elliptical restricted three body problem was "studied by Erdi [18]". The influence of the eccentricity of the orbit of the primary bodies with or without radiation pressure on the existence of the equilibrium points and there stability was "discussed to some extent by Khasan [12], [13], Pinyol [19], Floria [20], Halan and Rana [21], Markeev [22], Selaru and Dumitrescu [14], [15], Nayayan and Ramesh [23], [24]". The stability of triangular points in the elliptical restricted three body problem under radiating and oblate primaries was "studied by Singh and Umar [25], [26]".…”
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.
“…Furthermore, the nonlinear stability of the infinitesimal in the orbits or the size of the stable region around L 4 was "studied by Gyorgrey [16]" and the parametric resonance stability around L 4, in elliptical restricted three body problem was "studied by Erdi [18]". The influence of the eccentricity of the orbit of the primary bodies with or without radiation pressure on the existence of the equilibrium points and there stability was "discussed to some extent by Khasan [12], [13], Pinyol [19], Floria [20], Halan and Rana [21], Markeev [22], Selaru and Dumitrescu [14], [15], Nayayan and Ramesh [23], [24]". The stability of triangular points in the elliptical restricted three body problem under radiating and oblate primaries was "studied by Singh and Umar [25], [26]".…”
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.
“…[12], Narayan, A., Kumar, C.R. [13], Narayan, A., Singh, N. [14], Narayan, A., Usha, T. [15] , Singh, J., Aishetu, U. (2012), Singh, J., Aishetu, U.…”
This Paper deals with the effects of the radiation pressure and triaxiality of primaries on the stability of infinitesimal motion about triangular equilibrium points [ 4 , 5 ] 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.
“…The ER3BP are studied by [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26]. The present paper investigates the stability of the infinitesimal mass about the triangular equilibrium points in both resonance and non-resonance case satisfying…”
In this paper we study the non linear stability of the triangular librations points in ER3BP considering both the primaries as radiating and oblate. The study is carried out near the resonance frequency satisfying the conditions
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