and Computational Methods

doi: 10.18698/2309-3684-2022-2-88101

In this paper, optimization of the flight of a low-mass satellite from Earth orbit to the orbit of Venus using ion engines is considered. The first flight to the planet took place in 1961 by the Soviet automatic interplanetary station "Venus-1", which passed 100,000 kilometers from Venus. In addition, in 1962, the American station "Mariner-2" was flown. The most recent spacecraft launched to the planet was the European Space Agency's Venus Express in 2005, which flew to Venus in 153 days. When solving the current problem, the following assumptions were made: an interorbital flight is considered without taking into account the attraction of the planets, and the orbits of the planets are considered circular and lying in the same plane. The angle between the tangential velocity of the spacecraft and the thrust direction was chosen as the control. Optimization of satellite control was carried out using the Pontryagin maximum principle. The resulting boundary value problem for a system of ordinary differential equations was solved by a numerical method — the targeting method. Newton's method was used to solve systems of nonlinear algebraic equations. The calculation program was written using the C++ programming language. As a result of the work, it was possible to minimize the flight time between orbits, thus the operability of the shooting method for solving optimization problems was shown.

Mokletsov A. Issledovanie planety Venera kosmicheskimi apparatami [Exploration of the planet Venus by spacecraft]. RIA Novosti [RIA News] [Electronic resource], 2019. URL: https://ria.ru/20150611/1069063562.html (accessed: 01.03.2022)

Fuglesang C., Zetterling C.–M., Wilson C.F. Venus long-life surface package (VL2SP). Proceedings of the International Astronautical Congress, IAC, 2017, vol. 5, pp. 3035–3043.

Rossiyskaya Gazeta. Kogda sostoitsa polet na Veneru [When will the flight to Venus take place?] [Electronic resource]. URL: https://rg.ru/2018/10/09/kogda-sostoitsia-pervyj-polet-na-veneru.html (accessed: 10.02.2022)

Hi – News. Kak rabotaet ionnyj dvigatel' i gde on primenyaetsya? [How the ion engine works and where it is applied?] [Electronic resource]. URL: https://hi-news.ru/eto-interesno/kak-rabotaet-ionnyj-dvigatel-i-gde-on-primenyaetsya.html(accessed: 12.02.2022).

Morshneva I.V., Ovchinnikova S.N. Chislennoe reshenie kraevyh zadach dlyaobyknovennyh differencial'nyh uravnenij. Metod strel'by. Metodicheskie ukazaniya dlya studentov 3 i 4 kursov mekhmata [Numerical solution of edge problems for ordinary differential equations. The method of shooting. Methodological guidelines for students of the 3rd and 4th courses of the Faculty of Mechanics]. Rostov–on–Don, UPL RSU Publ., 2003, 29 p

Lietmann G. Optimization techniques: with applications to aerospace systems. Academic Press, 1962, 453 p.

Mozzhorina T.Yu. Numerical solution to problems of optimal control with switching by means of the shooting method. Mathematical modeling and Computational Methods, 2017, no. 2, pp. 94–106.

Vanko V.I., Ermoshina O.V., Kuvyrkin G.N. Variacionnoe ischislenie i optimal'noe upravlenie: ucheb. dlya vuzov [Calculus of variations and optimal control: Studies for universities]. Moscow, BMSTU Publ., 2006, 488 p.

Adesola O.A., Samson A.A., Ayomide O.A., Adekunle O.A. Dynamic computation of runge-kutta’s fourth-order algorithm for first and second order ordinary. International Journal of Computer Science Issues, 2015, vol. 12, iss. 3, pp. 211–218.

Ivanov A.P. Metod N'yutona resheniya nelinejnyh uravnenij i sistem uravnenij[Newton's method for solving nonlinear equations and systems of equations]. St. Petersburg, SPBU Publ., 2007, 9 p.

Fedorenko R.P. Priblizhennoe reshenie zadach optimal'nogo upravleniya [Approximate solution of optimal control problems]. Moscow, Nauka Publ., 1978, 486 p.

Semushin I.V. Vychislitel'nye metody algebry i ocenivaniya: uchebnoe posobie[Computational methods of algebra and evaluation: textbook]. Ulyanovsk, UlSTUPubl., 2011, 366 p

Мозжорина Т.Ю., Закуражная Д.А. Моделирование и оптимизация управления полетом космического аппарата с орбиты Земли на орбиту Венеры с помощью ионных двигателей. Математическое моделирование и численные методы, 2022, № 2, с. 90–103

Количество скачиваний: 157