Optimum transference from the collinear libration points of the earth-moon system

Optimized control strategies for minimization of time to move from one state vector to another in transferring from the collinear libration points in the earth-moon system are analytically defined. A Banach vector space and a dual vector space are formulated with respective norms whose product is employed to find maxima and minima for the equations of motion of a space vehicle. Control commands are then chosen to correspond with the set of minimum movement in terms of parametric equations of the trajectory. The minimum time required to make the transfer is then obtained.