Stabilization of collinear libration points in the earth-moon system

The translational-rotational motion of an orbital station in the Earth-Moon system is investigated. The orbital station is regarded as a body of variable composition with a solid shell and a low-thrust jet engine placed on it, having constant autonomous orientation in a system of coordinates rotating with the Moon. It is shown that, by means of a reaction acceleration of small and constant modulus, one can stabilize both the new libration points themselves and the positions of relative equilibrium of the orbital station. Each value of the reaction acceleration, depending on its orientation, corresponds to a whole family of libration points, surrounding the classical collinear point, but only some of them can be stable. It is shown that, when the ellipticity of the Moon's orbit is taken into account, periodic translational-rotational motions of the orbital station in the neighbourhood of these points can occur with a period equal to the period of rotation of the Moon.