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IssuesArchive of Issues2002-2pp.19-27

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S. V. Volkov, "Control of relative vibrations of a pendulum on a rotating platform," Mech. Solids. 37 (2), 19-27 (2002)
Year 2002 Volume 37 Number 2 Pages 19-27
Title Control of relative vibrations of a pendulum on a rotating platform
Author(s) S. V. Volkov (Moscow)
Abstract Kinematic equations are compiled for a design relative motion of two rigid bodies forming a mechanical system with two degrees of freedom. These equations are utilized for the synthesis of a feedback control supporting this motion. The properties of the design motion are specified in terms of a system of differential equations dot x=y, dot y=Y(x,y) having a prescribed set of singular trajectories and a prescribed structure of the entire phase space. The function Y(x,y) belongs to the class C1. The torque is determined which is applied to the axis of rotation of the platform and provides the asymptotic stability for the design vibratory motion of the pendulum mounted on this platform.
References
1.  G. V. Korenev, Essays on Mechanics of Purposeful Motion [in Russian], Nauka, Moscow, 1980.
2.  A. S. Galiullin, Inverse Dynamics Problems [in Russian], Nauka, Moscow, 1981.
3.  A. S. Galiullin, Methods for Solving Inverse Dynamics Problems [in Russian], Nauka, Moscow, 1986.
4.  A. S. Galiullin, I. A. Mukhametzyanov, R. G. Mukharlyamov, and V. D. Furasov, Construction of Equations of Design Motion for Controlled System [in Russian], Izd-vo UDN, Moscow, 1969.
5.  A. S. Galiullin (Editor), Design Motion of Mechanical Systems [in Russian], Izd-vo UDN, Moscow, 1971.
6.  A. S. Galiullin, "Construction of equations of motion," Differentsial'nye Uravneniya [Differential Equations], Vol. 12, No. 2, pp. 195-237, 1977.
7.  I. A. Mukhametzyanov and R. G. Mukharlyamov, Equations of Design Motions [in Russian], Izd-vo UDN, Moscow, 1986.
8.  I. A. Mukhametzyanov and R. G. Mukharlyamov, Equations of Design Motion, Optimization, and Estimates [in Russian], Izd-vo UDN, Moscow, 1986.
9.  N. P. Erugin, "Construction of the whole set of systems of differential equations having a prescribed integral curve," PMM [Applied Mathematics and Mechanics], Vol. 16, No. 6, pp. 659-670, 1952.
10.  M. I. Al'mukhamedov, "Inverse problem of the qualitative theory of differential equations," Izv. Vuzov. Matematika, No. 4, pp. 3-6, 1963.
11.  M. I. Al'mukhamedov, "On the construction of a differential equation having prescribed curves being its limit cycles," Izv. Vuzov. Matematika, No. 1, pp. 12-16, 1965.
12.  R. G. Mukharlyamov, "To the inverse problems of the qualitative theory of differential equations," Differentsial'nye Uravneniya [Differential Equations], Vol. 2, No. 10, pp. 1673-1681, 1967.
13.  S. V. Volkov, Construction of Differential Operators for Dynamical Systems [in Russian], Izd-vo RUDN, Moscow, 1999.
14.  M. Frommer, "Integral curves of a first-order ordinary differential equation in the neighborhood of a singular point having rational character," Uspekhi Matem. Nauk, No. 9, pp. 212-253, 1941.
Received 13 April 2001
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