Abstract
The problem of optimizing the interplanetary trajectories of a spacecraft (SC) with a solar electric propulsion system (SEPS) is examined. The problem of investigating the permissible power minimum of the solar electric propulsion power plant required for a successful flight is studied. Permissible ranges of thrust and exhaust velocity are analyzed for the given range of flight time and final mass of the spacecraft. The optimization is performed according to Portnyagin’s maximum principle, and the continuation method is used for reducing the boundary problem of maximal principle to the Cauchy problem and to study the solution/ parameters dependence. Such a combination results in the robust algorithm that reduces the problem of trajectory optimization to the numerical integration of differential equations by the continuation method.
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Chernous’ko, F.L., Otsenivanie fazovogo sostoyaniya dinamicheskikh sistem (The Way to Estimate Phase State of Dynamical Systems), Moscow: Nauka, 1988.
Grigoriev, I.S. and Grigoriev, K.G., The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: I, Cosmic Res., 2007a, vol. 45, no. 4, pp. 339–347.
Grigoriev, I.S. and Grigoriev, K.G., The use of solutions to problems of spacecraft trajectory optimization in impulse formulation when solving the problems of optimal control of trajectories of a spacecraft with limited thrust engine: II, Cosmic Res., 2007b, vol. 45, no. 6, pp. 553–563.
Irving, J.H., Low thrust flight: variable exhaust velocity in gravitational fields, in Space Technology, Seifert, H., Ed., New York: Wiley, 1959, chap. 10.
Lyness, J.N., Numerical algorithms based on the theory of complex variables, Proc. 22nd ACM Nat. Conf., Washington: Thompson Book, 1967a, pp. 124–134.
Lyness, J.N. and Moller, C.B., Numerical differentiation of analytic functions, SIAM J. Num. Anal., 1967b, vol. 4, pp. 202–210.
Malyshev, V.V. and Tychinskii, Yu.D., Construction of sets of attainability and maneuver optimization for lowthrust artificial satellites of the earth in a strong gravitational field, J. Comput. Syst. Sci. Int., 2005, vol. 44, no. 4, pp. 622–630.
Petukhov, V.G., Optimization of Multi-Orbit Transfers between Noncoplanar Elliptic Orbits, Cosmic Res., 2004, vol. 42, no. 3, pp. 250–268.
Petukhov, V.G., Optimization of interplanetary trajectories for spacecraft with ideally regulated engines using the continuation method, Cosmic Res., 2008, vol. 46, no. 3, pp. 219–232.
Petukhov, V.G., Method of continuation for optimization of interplanetary low-thrust trajectories, Cosmic Res., 2012, vol. 50, no. 3, pp. 249–261.
Petukhov, V.G., Minimum-thrust problem and its application to trajectory optimization with thrust switchings, Proc. IAC-13-C1.6.2, Beijing, 2013.
Polishchuk, G.M., Pichkhadze, K.M., Efanov, V.V., and Martynov, M.B., Space modules of Phobos-Grunt complex for prospective interplanetary stations, Sol. Syst. Res., 2011, vol. 45, no. 7, pp. 589–592.
Squire, W. and Trapp, G., Using complex variables to estimate derivatives of real functions, SIAM Rev., 1998, vol. 40, no. 1, pp. 110–112.
Standish, E.M., JPL Planetary and Lunar Ephemerides, DE405/LE405, Pasadena, CA: William Folkner, 1998, vol. 312, no. F-98-048, pp. 1–18.
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Original Russian Text © A.V. Ivanyukhin, V.G. Petukhov, 2015, published in Vestnik NPO imeni S.A. Lavochkina, 2015, No. 2, pp. 64–71.
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Ivanyukhin, A.V., Petukhov, V.G. Optimization of the interplanetary trajectories of spacecraft with a solar electric propulsion power plant of minimal power. Sol Syst Res 50, 552–559 (2016). https://doi.org/10.1134/S0038094616070078
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DOI: https://doi.org/10.1134/S0038094616070078