In this paper, optimization of the transfer of a low–mass satellite from Earth orbit to Mars orbit using ion thrusters is considered. The ion engine allows you to minimize fuel consumption and accelerate the spacecraft to fairly high speeds far from the planets of the solar system. The heliocentric section of the flight is subject to consideration. The task is to minimize the flight time. The following assumptions are made in the work: the orbits of the Earth and Mars are circular and lying in the same plane. The angle between the tangential velocity of the spacecraft in the heliocentric system and the direction of thrust action is selected as a control. When compiling the optimization algorithm, the Pontryagin maximum principle was used, which leads the optimization problem of a functional to a boundary value problem for a system of ordinary differential equations. The solution to the boundary value problem was found by one of the numerical methods — the false position method, which gives the most accurate results. The analysis of the results obtained is carried out and a comparison with the data obtained earlier in similar calculations by foreign authors by another numerical solution method is carried out. The conclusion is made about the efficiency of the false position method when solving such problems.
Мозжорина Т.Ю., Чуванова Л.О. Моделирование и оптимизация перелета спутников малой массы с Земной орбиты на орбиту Марса с помощью ионных двигателей. Математическое моделирование и численные методы, 2021, № 2, с. 54–67.