 | | 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: | | 11223 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8011
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| In English (Mech. Solids): | | 3212 |
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| << Previous article | Volume 47, Issue 2 / 2012 | Next article >> |
| A.V. Molodenkov and Ya.G. Sapunkov, "A New Class of Analytic Solutions in the Optimal Turn Problem for a Spherically Symmetric Body," Mech. Solids. 47 (2), 167-177 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
2 |
Pages |
167-177 |
| DOI |
10.3103/S0025654412020033 |
| Title |
A New Class of Analytic Solutions in the Optimal Turn Problem for a Spherically Symmetric Body |
| Author(s) |
A.V. Molodenkov (Institute for Precision Mechanics and Control, Russian Academy of Sciences Rabochaya 24, Saratov, 410028 Russia, molalexei@yandex.ru)
Ya.G. Sapunkov (Institute for Precision Mechanics and Control, Russian Academy of Sciences Rabochaya 24, Saratov, 410028 Russia, vem@info.sgu.ru) |
| Abstract |
The optimal turn problem for a rigid body with a spherical distribution of mass is considered in the quaternion setting. A functional combining the time and the integral magnitude of the control vector modulus used to turn the rigid body is used as the optimality criterion. This problem is solved analytically in the class of conical motions. An example of computations is given. |
| Keywords |
rigid body, spacecraft, optimal turn, analytic algorithm, regular precession |
| 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 Maneuvers,"
J. Guidance, Control, Dyn.
17 (2), 225-233 (1994). |
| 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. |
| 9. | A. V. Molodenkov and Ya. G. Sapunkov, "Special Control Regime in
Optimal Turn Problem of Spherically Symmetric Spacecraft," Izv.
Ross. Akad. Nauk. Teor. Sist. Upr., No. 6, 47-54 (2009) [J. Comp.
Syst. Sci. Int. (Engl. Transl.) 48 (6), 891-898 (2009)]. |
| 10. | L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and
E. F. Mishchenko, Mathematical Theory of Optimal Processes
(Fizmatgiz, Moscow, 1961) [in Russian]. |
|
| Received |
02 June 2010 |
| Link to Fulltext |
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