 | | 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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| << Previous article | Volume 41, Issue 5 / 2006 | Next article >> |
| M. Yu. Garnikhina and E. P. Kubyshkin, "Optimal control of rotation of a rigid body with a hereditary viscoelastic rod," Mech. Solids. 41 (5), 23-33 (2006) |
| Year |
2006 |
Volume |
41 |
Number |
5 |
Pages |
23-33 |
| Title |
Optimal control of rotation of a rigid body with a hereditary viscoelastic rod |
| Author(s) |
M. Yu. Garnikhina (Yaroslavl)
E. P. Kubyshkin (Yaroslavl) |
| Abstract |
We consider two problems on the optimal control of rotation of a system
consisting of a rigid body and a flexible rod rigidly attached to it. The
rod material is modeled by the rheological equation of a hereditary
viscoelastic solid [1]. This is the problem of bringing the system from an
initial state to a terminal state while minimizing a quadratic functional
of the control and the time optimization problem. We generalize the method
proposed in [2] for constructing optimal controls to the mechanical system
considered here. The construction of optimal controls uses only the
geometric characteristics of the system and the complex modulus of
elasticity of the rod material, which is determined experimentally. |
| References |
| 1. | Yu. N. Rabotnov, Elements of Hereditary Mechanics of Solids [in
Russian], Nauka, Moscow, 1977. |
| 2. | E. P. Kubyshkin, "Optimal control of rotation of a rigid body with
a flexible rod," PMM [Applied Mathematics and Mechanics], Vol. 56, No. 2,
pp. 240-249, 1992. |
| 3. | F. L. Chernousko, N. N. Bolotnik, and V. G. Gradteskii, Robot
Manipulators [in Russian], Nauka, Moscow, 1989. |
| 4. | S. I. Zlochevskii and E. P. Kubyshkin, "On the stabilization of a
satellite with flexible rods. I," Kosmicheskie Issledovaniya, Vol. 27,
No. 5, pp.643-651, 1989. |
| 5. | A. D. Ioffe and V. N. Tikhomirov, Theory of Extremal Problems [in
Russian], Nauka, Moscow, 1974. |
| 6. | F. Riesz and B. Sz.-Nagy, Lectures in Functional Analysis [Russian
translation], Mir, Moscow, 1979. |
| 7. | A. P. Prudnikov and Yu. A. Brychkov, Integrals and Series [in
Russian], Nauka, Moscow, 1981. |
|
| Received |
06 April 2004 |
| << Previous article | Volume 41, Issue 5 / 2006 | Next article >> |
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