Mathematical modeling of the space tug transfers between the Lagrange points of the Earth-Moon system

Abstract

The paper outlines the mathematical modeling of the L1-L2 and L2-L1 missions using electric propulsion. The variation problem of the low thrust spacecraft transfer optimization, with total flight time as the optimization criterion is considered. The locally optimal control programs were obtained by using the Fedorenko method to estimate the derivatives, the gradient method to optimize the control laws and the Runge-Kutta method for the numerical integration of the differential equation system. As the result of optimization, optimal control programs and corresponding trajectories were determined for certain values of acceleration and jet stream velocity of the propulsion system.