NON-LINEAR STABILITY OF THE TRIANGULAR EQUILIBRIUM POINTS IN THE ELLIPTIC RESTRICTED THREE BODY PROBLEM

The present paper analyzes the non-linear stability of the triangular equilibrium points of the elliptic restricted three body problem. The system consists of a radiating bigger primary and a triaxial smaller primary. The stability is analyzed in the presence of resonance for the case ω1 = 2ω2 and ω1 = 3ω2 and in the absence of resonances as well. The condition of stability have been found. It is observed that the equilibrium points are unstable for third order resonance and are stable for fourth order resonance for all values of radiation parameters q and triaxiality parameters σ1, σ2 and eccentricity e.