Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2014-5pp.495-505

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 49, Issue 5 / 2014 | Next article >>
A.V. Molodenkov and Ya.G. Sapunkov, "Solution of the Optimal Turn Problem for a Spherically Symmetric Rigid Body with Arbitrary Boundary Conditions in the Class of Generalized Conical Motions," Mech. Solids. 49 (5), 495-505 (2014)
Year 2014 Volume 49 Number 5 Pages 495-505
DOI 10.3103/S0025654414050021
Title Solution of the Optimal Turn Problem for a Spherically Symmetric Rigid Body with Arbitrary Boundary Conditions in the Class of Generalized Conical Motions
Author(s) A.V. Molodenkov (Institute for Precision Mechanics and Control, Russian Academy of Sciences, ul. Rabochaya 24, Saratov, 410028 Russia, iptmuran@san.ru, molalexei@yandex.ru)
Ya.G. Sapunkov (Chernyshevskii Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia, vem@info.sgu.ru)
Abstract We consider the problem of time- and energy consumption-optimal turn of a rigid body with spherical mass distribution under arbitrary boundary conditions on the angular position and angular velocity of the rigid body. The optimal turn problem is modified in the class of generalized conical motions, which allows one to obtain closed-form solutions for equations of motion with arbitrary constants. Thus, solving the optimal control boundary value problem is reduced to solving a system of nonlinear algebraic equations for the constants. Numerical examples are considered to illustrate the proximity between the solutions of the traditional and modified problems of optimal turn of a rigid body.
Keywords rigid body, spacecraft, optimal turn, arbitrary boundary conditions
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].
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 Turn of a Rigid Body with a Single Axis of Symmetry," 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 Problem of Optimal Turn of 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 Problem of Optimal Turn of 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, "Solution of the Problem of Optimal Turn of a Spherically Symmetric Spacecraft with Constrained Pulse Control under Arbitrary Boundary Conditions," Izv. Ross. Akad. Nauk. Teor. Sist. Upr., No. 2, 185-196 (2004) [J. Comp. Syst. Sci. Int. (Engl. Transl.) 43 (2), 317-336 (2004)].
10.  A. V. Molodenkov and Ya. G. Sapunkov, "A New Class of Analytic Solutions in the Optimal Turn 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)].
11.  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)].
12.  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).
13.  Ya. G. Sapunkov and A. V. Molodenkov, "The Investigation of Characteristics of Distant Sounding System of the Earth with the Help of Cosmic Device," Supplement for Mekhatron. Avtomatiz. Upravl.: Avtomatich. Avtomatizir. Upr. Let. App. No. 6, 10-15 (2008).
14.  G. J. Lastman, "A Shooting Method for Solving Two-Point Boundary-Value Problems Arising from Nonsingular Bang-Bang Optimal Control Problems," Int. J. Contr. 27 (4), 513-524 (1978).
15.  F. Li and P. M. Bainum, "Numerical Approach for Solving Rigid Spacecraft Minimum Time Attitude Maneuvers," J. Guid. Contr. Dynam. 13 (1), 38-45 (1978).
Received 09 July 2012
Link to Fulltext
<< Previous article | Volume 49, Issue 5 / 2014 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100