Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
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IssuesArchive of Issues2010-4pp.401-405

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S.A. Agafonov, "The stability and stabilization of the motion of non-conservative mechanical systems," J. Appl. Math. Mech. 74 (4), 401-405 (2010)
Year 2010 Volume 74 Issue 4 Pages 401-405
Title The stability and stabilization of the motion of non-conservative mechanical systems
Author(s) S.A. Agafonov (Moscow, Russia,
Abstract Two stability problems are solved. In the first, the stability of mechanical systems, on which dissipative, gyroscopic, potential and positional non-conservative forces (systems of general form) act, is investigated. The stability is considered in the case when the potential energy has a maximum at equilibrium. The condition for asymptotic stability is obtained by constructing Lyapunov's function. In the second problem, the possibility of stabilizing a gyroscopic system with two degrees of freedom up to asymptotic stability using non-linear dissipative and positional non-conservative forces is investigated. Stability of the gyroscopic system is achieved by gyroscopic stabilization. The stability conditions are obtained in terms of the system parameters. Cases when the gyroscopic stabilization is disrupted by these non-linear forces are indicated.
Received 10 December 2008
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