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 L_{4} 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 A_{1} ,
A_{1} , A_{2} , P and P ,
where
A_{1} , A_{1} and A_{2 }, 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.