On the stabilization of relative equilibrium of the orbital station at the collinear libration point beyond the moon

Considered a problem for the relative equilibrium stabilization of the orbital station at the unstable collinear libration point L
₂
in the Earth-Moon system with a small change of the reaction engine acceleration (constant in magnitude) rigidly attached to the station. It is shown, that with a small movement of the station's center of mass relatively to the point L
₂
in the station's parameter space there is a region in which its relative equilibrium in its translation-rotation motion is stable in the first approximation.