Rajiv Aggarwal, Z. A. Taqvi and Iqbal Ahmad
Department of Mathematics, Jamia Mil lia Islamia, New Delhi 110 025, India

Abstract. We have investigated the non-linear stability of the triangular libration point L4 of the Restricted three body problem under the presence of the third and fourth order resonances, when the bigger primary is an oblate body and the smaller a triaxial body and both are source of radiation. It is found through Markeev's theorem that L₄ is always unstable in the third order resonance case and stable or unstable in the fourth order resonance case depending upon the values of the parameters A₁ , A₁ , A₂ , P and P , where A₁ , A₁ and A₂ , depends upon the lengths of the semi axes of the primaries and P and P are the radiation parameters.

Keywords: : Restricted three body problem, axis symmetric body, libration points, non-linear stability, Markeev's theorem.

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