519.6 Modeling and optimization of low–mass satellite control when flying from Earth orbit to Mars orbit under a solar sail

Mozzhorina T. Y. (Bauman Moscow State Technical University), Rakhmankulov D. A. (Bauman Moscow State Technical University)

SOLAR SAIL, THE FALSE POSITION METHOD, BOUNDARY VALUE PROBLEMS OF ORDINARY DIFFERENTIAL EQUATIONS, OPTIMAL CONTROL, PONTRYAGIN'S MAXIMUM PRINCIPLE, FLIGHT BETWEEN THE ORBITS OF THE EARTH AND MARS


doi: 10.18698/2309-3684-2021-3-7487


In this paper, the optimization of the transfer of a low–mass satellite from the Earth's orbit to the Mars orbit under a solar sail is considered. Optimization of the control of the pitch angle of the solar sail is carried out using the Pontryagin maximum principle while minimizing the flight time. In contrast to previous works on this topic, the solution of the boundary value problem, to the solution of which the maximum principle is reduced, was obtained by the false position method. The calculation program is written in the C++ programming language. Despite the computational difficulties arising when using the false position method, it was possible to achieve good convergence of the Newton method underlying the algorithm. The analysis of the accuracy of the results obtained is carried out and the possibility of using the false position method in solving such problems is shown. A comparison is made with the data of previously published works. Despite some assumptions used in the development of the calculation algorithm, the work has its value in terms of assessing the possibility of using the false position method, which gives the most accurate numerical optimization results.


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