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IssuesArchive of Issues2016-2pp.135-147

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A.V. Molodenkov and Ya.G. Sapunkov, "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 (2), 135-147 (2016)
Year 2016 Volume 51 Number 2 Pages 135-147
DOI 10.3103/S0025654416020011
Title Analytical Solution of the Optimal Attitude Maneuver Problem with a Combined Objective Functional for a Rigid Body in the Class of Conical Motions
Author(s) A.V. Molodenkov (Institute for Precision Mechanics and Control, Russian Academy of Sciences, ul. Rabochaya 24, Saratov, 410028 Russia, molalexei@yandex.ru)
Ya.G. Sapunkov (Institute for Precision Mechanics and Control, Russian Academy of Sciences, ul. Rabochaya 24, Saratov, 410028 Russia)
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.
Keywords rigid body, spacecraft, optimal attitude maneuver, conical motion
References
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2.  S. L. Scrivener and R. C. Thompson, ""Survey of Time-Optimal Attitude Maneuvers," J. Guid. Contr. Dynam. 17 (2), 225-233.
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.)].
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.)].
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.)].
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)].
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].
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].
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)].
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)].
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).
12.  Yu. N. Chelnokov, Quaternion and Biquaternion Models and Methods of Mechanics of Rigid Body and Their Applications (Fizmatlit, Moscow, 2006) [in Russian].
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)].
14.  Ya. G. Sapunkov and A. V. Molodenkov, "The Investigation of Characteristics of Distant Sounding System of 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).
Received 20 January 2014
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