 | | 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
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| In English (Mech. Solids): | | 4810 |
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| A.N. Sirotin, "Flat Turn as an Admissible Extremal in the Optimal Rotation Control Problem for an Asymmetric Body," Mech. Solids. 47 (1), 1-18 (2012) |
| Year |
2012 |
Volume |
47 |
Number |
1 |
Pages |
1-18 |
| DOI |
10.3103/S0025654412010013 |
| Title |
Flat Turn as an Admissible Extremal in the Optimal Rotation Control Problem for an Asymmetric Body |
| Author(s) |
A.N. Sirotin (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993 Russia, asirotin2@yandex.ru) |
| Abstract |
The problem of optimal control of rotation of an asymmetric rigid body is studied.
An integrally quadratic functional characterizing the total energy costs
is taken as the criterion.
It is shown that, under certain conditions, the problem has a nontrivial extremal
corresponding to a 180-degree flat turn,
i.e., rotation about an axis fixed in the inertial space.
The obtained results are based on an analysis of the equations
arising after the application of the Pontryagin maximum principle (PMP) formalism. |
| Keywords |
optimal control, rotation, asymmetric rigid body, maximum principle |
| References |
| 1. | A. N. Sirotin,
"Analytical Solutions in the Problem of the Optimal Control of the Rotation of an Axisymmetric Body,"
Prikl. Mat. Mekh.
70 (2), 225-235 (2006)
[J. Appl. Math. Mech. (Engl. Transl.)
70 (2), 199-209 (2006)]. |
| 2. | K. B. Alekseev,
Extensive Control of Space Craft Attitude
(Mashinostroenie, Moscow, 1977)
[in Russian]. |
| 3. | A. N. Sirotin,
"The Existence of Smooth Solutions in a Problem of the Optimal
Control of the Rotation of an Axisymmetric Rigid Body,"
Prikl. Mat. Mekh.
72 (3), 399-409 (2008)
[J. Appl. Math. Mech. (Engl. Transl.)
72 (3), 270-278 (2008)]. |
| 4. | E. Kamke,
Handbook on Ordinary Differential Equations
(Fizmatgiz, Moscow, 1961). |
| 5. | A. I. Lurie,
Analytic Mechanics
(Fizmatgiz, Moscow, 1961; Springer, Berlin, 2001). |
| 6. | L. D. Landau and E. M. Lifshitz,
Course of Theoretical Physics, Vol. 1: Mechanics
(Nauka, Moscow, 1965; Pergamon Press, Oxford, 1976). |
|
| Received |
16 June 2009 |
| Link to Fulltext |
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