Optimization of trajectories for a spacecraft with an electric rocket engine of low thrust

The paper considers a problem of optimizing the trajectories for a spacecraft (SC) with an electric rocket engine and making a direct flight (without the gravity assists) between two celestial bodies. The program of the control for the electric propulsion engine is found using the Pontryagin's maximum principle for two mathematical models of thrust: ideal thrust and limited one. The nonlinear two-point boundary-value problem of the maximum principle is solved using modified Newton's method. The peculiarities of solving this problem are given. The fundamental difficulties caused by a discontinuous profile of limited thrust are overcome using the method of logarithmic smoothing. The elements of the sensitivity matrix are determined by integrating the corresponding systems of differential equations in deviations. There is also given a numerical example that illustrates the application of the developed technique to the problem of optimizing the SC flight from Earth to asteroid Apophis.