Abstract. Trajectories of the Lagrangian point L4 and the Lyapunov Characteristic Exponents (LCEs) are computed numerically. The dynamical behavior of near by trajectories is estimated by LCEs for various values of parameters. The values of LCEs remain positive for all the cases and depend on the initial deviation vector as well as the re-normalization time step. It is noticed that the trajectories are chaotic in nature and the L4 is asymptotically stable. The effect of radiation pressure, oblateness and mass of the belt are also examined in the present model