Optimal transfer from the lagrangian points

The transfer from the equilateral Lagrangian points of the Earth-Moon system is analysed. The final states of the velocity of the space vehicles and of the rotation velocity of the propulsion vector are assumed given. The trajectory which ensures the transfer in optimal time consists of three arcs. On this trajectory the rotation velocity of the direction of the propulsion has the extremal value or corresponds to the Lawden's tangent law. The use of the matching of the arcs together with transversality conditions and final conditions determines the constants of integration and the evolution time. The resulting parametric equations of the optimal trajectory are of integral form.