 | | 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: | | 12804 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8044
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| In English (Mech. Solids): | | 4760 |
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| << Previous article | Volume 49, Issue 5 / 2014 | Next article >> |
| V.G. Biryukov and Yu.N. Chelnokov, "Construction of Optimal Laws of Variation of the Angular Momentum Vector of a Rigid Body," Mech. Solids. 49 (5), 479-494 (2014) |
| Year |
2014 |
Volume |
49 |
Number |
5 |
Pages |
479-494 |
| DOI |
10.3103/S002565441405001X |
| Title |
Construction of Optimal Laws of Variation of the Angular Momentum Vector of a Rigid Body |
| Author(s) |
V.G. Biryukov (Chernyshevskii Saratov State University, ul. Astrakhanskaya 83, Saratov, 410012 Russia; Institute for Precision Mechanics and Control Problems, ul. Rabochaya 24, Saratov, 410028 Russia, biryukovvg@mail.ru, biryukovvg@gmail.ru)
Yu.N. Chelnokov (Institute for Precision Mechanics and Control Problems, ul. Rabochaya 24, Saratov, 410028 Russia, chelnokovyun@info.sgu.ru) |
| Abstract |
We consider the problem of constructing optimal preset laws of variation of the angular momentum vector of a rigid body taking the body from an arbitrary initial angular position to the required terminal angular position in a given time. We minimize an integral quadratic performance functional whose integrand is a weighted sum of squared projections of the angular momentum vector of the rigid body. We use the Pontryagin maximum principle to derive necessary optimality conditions. In the case of a spherically symmetric rigid body, the problem has a well-known analytic solution. In the case where the body has a dynamic symmetry axis, the obtained boundary value optimization problem is reduced to a system of two nonlinear algebraic equations. For a rigid body with an arbitrary mass distribution, optimal control laws are obtained in the form of elliptic functions. We discuss the laws of controlled motion and applications of the constructed preset laws in systems of attitude control by external control torques or rotating flywheels. |
| Keywords |
quaternion, angular momentum, rigid body, optimal control |
| References |
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|
| Received |
08 February 2012 |
| Link to Fulltext |
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