Short term evolution of artificial satellites

When the elimination of the parallax and the elimination of the perigee is applied to the zonal problem of the artificial satellite, a one-degree of f reedom Hamiltonian is obtained. The classical way to integrate this Hamilto nian is by applying the Delaunay normalization, however, changing the time to the perturbed true anomaly and the variable to the inverse of the distan ce, the Hamilton equations become a perturbed harmonic oscillator. In this paper we apply the Krylov-Bogoliubov-Mitropolsky (KBM) method to integrate the perturbed harmonic oscillator as an alternative method to the Delaunay normalization. This method has no problem with small eccentricities and inc linations, and shows good numerical results in the evaluation of ephemeris of satellites.