Construction of optimum controls and trajectories of motion of the center of masses of a spacecraft equipped with the solar sail and low-thrust engine, using quaternions and Kustaanheimo-Stiefel variables

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• 作者：Ya. G. Sapunkov (1)
  Yu. N. Chelnokov (1)
  
• 刊名：Cosmic Research
• 出版年：2014
• 出版时间：November 2014
• 年：2014
• 卷：52
• 期：6
• 页码：450-460
• 全文大小：437 KB
• 参考文献：1. Chelnokov, Yu.N. and Sapunkov, Ya.G., Design of optimal control strategies and trajectories of a spacecraft with the regular quaternion equations of the two-body problem, / Cosmic Research, 1996, vol. 34, no. 2, pp. 137-45.
  2. Sapunkov, Ya.G., The use of KS-variables in the problem of spacecraft optimum control, / Cosmic Research, 1996, vol. 34, no. 4, pp. 395-00.
  3. Chelnokov, Yu.N. and Yurko, V.A., Quaternion design of optimum control and trajectories of motion of a spacecraft in Newtonian gravitational field, / Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, 1996, no. 6, pp. 3-3.
  4. Sapunkov, Ya.G., Optimal control over motion of a spacecraft with combined thrust, in / Matematika. Mekhanika. Sb. nauch. tr. (Mathematics and Mechanics: Collection of Scientific Papers), Saratov: Izd. Saratov. Univ., 2009, issue 11, pp. 129-32.
  5. Sapunkov, Ya.G., Solving the problems of optimal control for a spacecraft with restricted and impulsive thrust in KS-variables, / Mekhatronika, Avtomatizatsiya, Upravlenie, 2010, no. 3, pp. 73-8.
  6. Chelnokov, Yu.N., / Kvaternionnye modeli i metody dinamiki, navigatsii i upravleniya dvizheniem (Quaternion Models and Methods in Dynamics, Navigation, and Motion Control), Moscow: Fizmatlit, 2011.
  7. Abalakin, V.K., Aksenov, E.P., Grebenikov, E.A., Demin, V.G., and Ryabov, Yu.A., / Spravochnoe rukovodstvo po nebesnoi mekhanike i astrodinamike (Handbook of Celestial Mechanics and Astrodynamics), Moscow: Nauka, 1976.
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  10. Branets, V.N. and Shmyglevskii, I.P., / Primenenie kvaternionov v zadachakh orientatsii tverdogo tela (Application of Quaternions in Problems of Solid Body Orientation), Moscow: Nauka, 1973.
  11. Chelnokov, Yu.N., / Kvaternionnye i bikvaternionnye modeli i metody mekhaniki tverdogo tela i ikh prilozheniya: Geometriya i kinematika dvizheniya (Quaternion and Bi-Quaternion Models and Methods of Solid Body Mechanics and Their Application: Geometry and Kinematics of Motion), Moscow: Fizmatlit, 2005.
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  13. Chelnokov, Yu.N., On regularization of equations of the three-dimensional two-body problem, / Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 1981, no. 6, pp. 12-1.
  14. Chelnokov, Yu.N., Regular equations of the threedimensional two-body problem, / Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, 1984, no. 1, pp. 151-58.
  15. Chelnokov, Yu.N., Application of quaternions in the theory of orbital motion of artificial satellites. I, / Cosmic Research, 1992, vol. 30, no. 6, pp. 612-21.
  16. Chelnokov, Yu.N., Application of quaternions in the theory of orbital motion of artificial satellites. II, / Cosmic Research, 1993, vol. 31, no. 3, pp. 409-18.
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• 作者单位：Ya. G. Sapunkov (1)
  Yu. N. Chelnokov (1)
  
  1. Institute of Precision Mechanics and Control Problems of the Russian Academy of Sciences, Chernyshevsky Saratov State University, Rabochaya ul., Saratov, 410028, Russia
  
• ISSN：1608-3075

文摘

The problem of optimum rendezvous of a controllable spacecraft (SC) with an uncontrollable spacecraft, moving over a Keplerian elliptic orbit in the gravitational field of the Sun, is considered. Control of the SC is performed using a solar sail and low-thrust engine. For solving the problem, the regular quaternion equations of the two-body problem with the Kustaanheimo-Stiefel variables and the Pontryagin maximum principle are used. The combined integral quality functional, which characterizes energy consumption for controllable SC transition from an initial to final state and the time spent for this transition, is used as a minimized functional. The differential boundary-value optimization problems are formulated, and their first integrals are found. Examples of numerical solution of problems are presented. The paper develops the application [1-] of quaternion regular equations with the Kustaanheimo-Stiefel variables in the space flight mechanics.