Science missions around natural satellites require low eccentricity and high inclination orbits. These orbits are unstable because of the planetary perturbations, making control necessary to reach the required mission lifetime. Dynamical systems theory helps in improving lifetimes reducing fuel consumption. After a double averaging of the 3-DOF model, the initial conditions are chosen so that the orbit follows the stable-unstable manifold path of an equilibria of the 1-DOF reduced problem. Corresponding initial conditions in the non-averaged problem are easily computed from the explicit transformations provided by the Lie-Deprit perturbation method.