An analytical investigation is performed to deter¬mine the properties of the motion of a small body in the vicinity of the stable libration points of the Earth-Moon system. On the basis of a first-order analysis of the equations of motion of the restricted three-body problem, an explicit solution is obtained for the position and velocity components of the motion as a function of the initial conditions. The results of the explicit solution lead to a determination of the properties of the motion as a, function of the initial conditions. The properties so determined include the position in orbit and the velocity components as a function of time, the properties of the component elliptical motions which comprise the resultant motion, the existence of periodic elliptical orbits through proper choice of initial conditions, and the limits of the motion.
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