Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
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Kozlov E. A., Chelnokov Y. N., Pankratov I. A. Investigation of the Problem of Optimal Correction of Angular Elements of the Spacecraft Orbit Using Quaternion Differential Equation of Orbit Orientation. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2016, vol. 16, iss. 3, pp. 336-344. DOI: 10.18500/1816-9791-2016-16-3-336-344, EDN: WMIIJF

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Investigation of the Problem of Optimal Correction of Angular Elements of the Spacecraft Orbit Using Quaternion Differential Equation of Orbit Orientation

Kozlov Evgeny Aleksandrovich, Saratov State University
Chelnokov Yurii Nikolaevich, Saratov State University
Pankratov Il'ya Alekseevich, Saratov State University

In this paper we consider the problem of optimal correction of angular elements of the spacecraft orbit. Control (jet thrust vector orthogonal to the plane of the orbit) is limited by absolute value. The combined quality functional characterizes the amount of time and energy consumption. With the help of the Pontryagin maximum principle and quaternion differential equation of the spacecraft orbit orientation, we have formulated differential boundary value problem of correction of the angular elements of the spacecraft orbit. Optimal control law, transversality conditions, not containing Lagrange multipliers, examples of the numerical solution of the problem are given.

  1. Pontriagin L. S., Boltianskii V. G., Gamkrelidze R. V., Mishchenko E. F. Matematicheskaia teoriia optimal’nykh protsessov [The mathematical theory of optimal processes]. Moscow, Nauka, 1983, 393 p. (in Russian).
  2. Chelnokov Yu. N. Optimal reorientation of a spacecraft’s orbit using a jet thrust orthogonal to the orbital plane. J. Appl. Math. Mech., 2012, vol. 76, iss. 6, pp. 646–657. DOI: https://doi.org/10.1016/j.jappmathmech.2013.02.002.
  3. Pankratov I. A., Sapunkov Ya. G., Chelnokov Yu. N. About a problem of spacecraft’s orbit optimal reorientation. Izv. Saratov Univ. (N. S.), Ser. Math. Mech. Inform., 2012, vol. 12, iss. 3, pp. 87–95 (in Russian).
  4. Abalakin V. K., Aksenov E. P., Grebennikov E. A., Demin V. G., Ryabov Yu. A. Spravocnoe rukovodstvo po nebesnoi mehanike i astrodinamike [Handbook on Celestial Mechanics and Astrodynamics]. Moscow, Nauka, 1976, 864 p. (in Russian).
  5. Chelnokov Yu. N. Kvaternionnye i bikvaternionnye modeli i metody mehaniki tverdogo tela i ih prilozhenija. Geometrija i kinematika dvizhenija [Quaternion and Biquaternion Models and Methods of Mechanics of a Rigid Body and their Applications. Geometry and Kinematics of Motion]. Moscow, Fizmatlit, 2006, 512 p. (in Russian).
  6. Deprit A. Ideal frames for perturbed keplerian motions. Celestial Mechanics, 1976, vol. 13, no. 2, pp. 253–262.
  7. Brumberg V. A. Analytical techniques of celestial mechanics. Berlin, Springer-Verlag, 1995, 236 p. (Rus. ed.: Brumberg V.A. Analiticheskie algoritmy nebesnoj mehaniki. Moscow, Nauka, 1980, 208 p.)
  8. Chelnokov Yu. N., Pankratov I. A., Sapunkov Ya. G. Optimal reorientation of spacecraft orbit. Archives of Control Sciences, 2014, vol. 24, no. 2, pp. 119–128.
  9. Branets V. N., Shmyglevskii I. P. Primenenie kvaternionov v zadachakh orientatsii tverdogo tela [Application of Quaternions in Problems of Orientation of a Rigid Body]. Moscow, Nauka, 1973, 320 p. (in Russian).
  10. Moiseev N. N. Chislennye metody v teorii optimal’nyh sistem [Numerical methods in the theory of optimal systems]. Moscow, Nauka, 1971, 424 p. (in Russian).
  11. Bordovitzyna T. V. Sovremennye chislennye metody v zadachah nebesnoj mehaniki [Modern numerical methods in problems of celestial mechanics]. Moscow, Nauka, 1984, 136 p. (in Russian).