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Analytical solution of the optimal attitude maneuver problem with a combined objective functional for a rigid body in the class of conical motions

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Abstract

The optimal attitude maneuver control problem without control constraints is studied in the quaternion statement for a rigid body with a spherical mass distribution. The performance criterion is given by a functional combining the time and energy used for the attitude maneuver. A new analytical solution in the class of conical motions is obtained for this problem on the basis of the Pontryagin maximum principle.

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References

  1. V. N. Branets and I. P. Shmyglevskii, Application of Quaternions in Problems of Orientation of a Rigid Body (Nauka, Moscow, 1973) [in Russian].

    MATH  Google Scholar 

  2. S. L. Scrivener and R. C. Thompson, “Survey of Time-Optimal Attitude Maneuvers,” J. Guid. Contr. Dynam. 17 (2), 225–233 (1993).

    Article  ADS  Google Scholar 

  3. Yu. N. Chelnokov, “Quaternion Solution of Kinematic Problems in Rigid Body Orientation Control — Equations of Motion, Problem Statement, Programmed Motion, and Control,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 4, 7–14 (1993) [Mech. Solids (Engl. Transl.)].

    Google Scholar 

  4. V. N. Branets, M. B. Chertok, and Yu. V. Kaznacheev, “Optimal Attitude Maneuver of a Rigid Body with a Single Symmetry Axis,” Kosmich. Issledovaniya 22 (3), 352–360 (1984) [Cosmic Res. (Engl. Transl.)].

    Google Scholar 

  5. A. N. Sirotin, “Optimal Control of Retargeting of a Symmetrically Rigid Body from a Rest Position to a Rest Position,” Izv. Akad. Nauk SSSR.Mekh. Tverd. Tela, No. 1, 36–47 (1989) [Mech. Solids (Engl. Transl.)].

    ADS  Google Scholar 

  6. A. N. Sirotin, “Time-Optimal Retargeting of a Rotating Spherically Symmetric Body with Stopping Its Motion,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 3, 18–27 (1997) [Mech. Solids (Engl. Transl.) 32 (3), 14–21 (1997)].

    Google Scholar 

  7. A. V. Molodenkov, “Quaternion Solution of the Optimal Attitude Maneuver Problem for a Rigid Body with Spherical Distribution of Mass,” in Problems of Mechanics and Control. Collection of Scientific Papers (PGU, Perm, 1995), pp. 122–131 [in Russian].

    Google Scholar 

  8. A. V. Molodenkov, “Solution of the Optimal Attitude Maneuver Problem for a Spherically Symmetric Spacecraft in One Special Case,” in Proc. 6th Intern. Conf. “System Analysis and Control of Extraterrestrial Complexes”, Evpatoriya, Krym (MAI,Moscow, 2001), p. 42 [in Russian].

    Google Scholar 

  9. A. V. Molodenkov and Ya. G. Sapunkov, “A New Class of Analytical Solutions in the Optimal Attitude Maneuver Problem for a Spherically Symmetric Body,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 16–27 (2012) [Mech. Solids (Engl. Transl.) 47 (2), 167–177 (2012)].

    Google Scholar 

  10. A. V. Molodenkov and Ya. G. Sapunkov, “Solution of the Optimal Attitude Maneuver Problem for a Spherically Symmetric Rigid Body with Arbitrary Boundary Conditions in the Class of Generalized Conical Motions,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 5, 22–34 (2014) [Mech. Solids (Engl. Transl.) 49 (5), 495–505 (2014)].

    MATH  Google Scholar 

  11. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Fizmatgiz, Moscow, 1961; Gordon & Breach Sci. Publ., New York, 1986).

    Google Scholar 

  12. Yu. N. Chelnokov, Quaternion and BiquaternionModels andMethods ofMechanics of Rigid Body and Their Applications (Fizmatlit, Moscow, 2006) [in Russian].

    Google Scholar 

  13. A. V. Molodenkov, “On the Solution of the Darboux Problem,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 2, 3–13 (2007) [Mech. Solids (Engl. Transl.) 42 (2), 167–176 (2007)].

    Google Scholar 

  14. Ya. G. Sapunkov and A.V. Molodenkov, “The Investigation of Characteristics of Distant Sounding Systemof the Earth with the Help of Cosmic Device,” “Numerical Solution of the Problem of Optimal Reorientation of a Rotating Spacecraft,” Supplement for Mekhatron. Avtomatiz. Upravl.: Avtomatich. Avtomatizir. Upr. Let. App. No. 6, 10–15 (2008).

    Google Scholar 

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Authors and Affiliations

  1. Institute for Precision Mechanics and Control, Russian Academy of Sciences, ul. Rabochaya 24, Saratov, 410028, Russia

    A. V. Molodenkov & Ya. G. Sapunkov

Authors
  1. A. V. Molodenkov
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  2. Ya. G. Sapunkov
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Correspondence to A. V. Molodenkov.

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Original Russian Text © A.V. Molodenkov, Ya.G. Sapunkov, 2016, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2016, No. 2, pp. 3–16.

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Molodenkov, A.V., Sapunkov, Y.G. Analytical solution of the optimal attitude maneuver problem with a combined objective functional for a rigid body in the class of conical motions. Mech. Solids 51, 135–147 (2016). https://doi.org/10.3103/S0025654416020011

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  • DOI: https://doi.org/10.3103/S0025654416020011

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