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IssuesArchive of Issues2006-5pp.23-33

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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
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