Analysis on nonlinear stability of the triangular libration points for radiating and oblate primaries in ER3BP

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 in resonance as well as non resonance case. The study is conducted for various values of radiation pressure and oblateness parameters. It is observed that the case corresponds to the boundary region of the stability for the system Further, it is examined that the system experiences resonance at for different values of radiation pressures and oblateness parameter. In non resonance case, it is observed that the equilibrium points are stable. In resonance case, for and the triangular equilibrium points are unstable. In case, when for some values of radiation pressure and oblateness parameter, it is stable and for some it is unstable. The model is best suited to the binary systems (Achird, Luyten, α Cen AB, Kruger- 60, Xi- Bootis).