 | | 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, "On Some Geometric Properties of Extremals in the Optimal Retargeting Problem for Spherically Symmetric Rigid Bodies," Mech. Solids. 44 (5), 663-670 (2009) |
| Year |
2009 |
Volume |
44 |
Number |
5 |
Pages |
663-670 |
| DOI |
10.3103/S0025654409050021 |
| Title |
On Some Geometric Properties of Extremals in the Optimal Retargeting Problem for Spherically Symmetric Rigid Bodies |
| Author(s) |
A.N. Sirotin (Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993 Russia, asirotin2@mail.ru) |
| Abstract |
We study an optimal control problem for the spatial retargeting of a rotating rigid body with unit tensor of inertia. We find new geometric properties of the extremals in this variational problem in the nondegenerate case. We give a detailed description of the extremal "collapse" effect and its relation to the planar manoeuvre. We also show that each extremal has some rank properties. The results are based on the analysis of the system of equations obtained by applying the formalism of the Pontryagin maximum principle and on the use of first integrals. |
| Keywords |
optimal control, rotation, asymmetric rigid body, maximum principle |
| References |
| 1. | 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)]. |
| 2. | A. N. Sirotin,
"The Problem of Power-Consumption-Optimal Retargeting with Simultaneous Retardation of a Spherically Symmetric Body with an Unspecified Time,"
Prikl. Mat. Mekh.
68 (5), 833-846 (2004)
[J. Appl. Math. Mech. (Engl. Transl.)
68 (5), 743-755 (2004)]. |
| 3. | 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)]. |
| 4. | L. S. Pontryagin,
Ordinary Differential Equations
(Nauka, Moscow, 1970)
[in Russian]. |
|
| Received |
17 October 2007 |
| Link to Fulltext |
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