Non- linear stability of triangular librations points in circular restricted three body under radiating and oblate primaries in presence of resonance

The nonlinear stability of the triangular librations points is studied in the presence resonance considering both the primaries as radiating and oblate. The study is carried out for various values of radiation pressure and oblateness parameter in general and binary systems in particular. It is found that the normal forms of the Hamiltonian contains both the resonance cases; ω 1 = 2ω 2 and ω 1 = 3ω 2 . The case ω 1 = ω 2 corresponds to the boundary region of the stability for the system.It is investigated that for the motion is unstable for third order resonance but stable for fourth order resonance.