This article presents a study of nonlinear motion of an electric propulsion spacecraft. Spacecraft transfers between the libration points L1 and L2 of the Earth-Moon system are analyzed. The influence of the shaded areas and gravitational effects of the Earth, the Moon and the Sun is taken into account. The mathematical model of the transfers is described within the barycentric coordinate frame. The exact optimal solution of the problem is obtained using Pontryagin’s maximum principle formalism and the numerical solution of the boundary value problem. The method of optimizing the parameters and controls of interplanetary trajectories of the spacecraft based on the optimization of dynamic system components and on Fedorenko’s method of sequential linearization is applied in this study. This method allows limitations on composite functions with Fréchet derivatives. As the results of the simulation, the control laws and corresponding trajectories are obtained.
The Stepwise Control Laws in the Problem of the Motion Optimization of the Electric Powered Transfers in the Earth-Moon System, Including L1-L2 and L2-L1 Missions