 | | 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 |
Archive of Issues
| Total articles in the database: | | 12854 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
|
| In English (Mech. Solids): | | 4810 |
|
| << 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 >> |
|
 If you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter
|
|
Russian 
English