Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
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in January 1966
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Print ISSN 0025-6544
Online ISSN 1934-7936

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G. G. Denisov and V. V. Novikov, "A problem of gyroscopic stabilization of mechanical systems," Mech. Solids. 41 (3), 8-11 (2006)
Year 2006 Volume 41 Number 3 Pages 8-11
Title A problem of gyroscopic stabilization of mechanical systems
Author(s) G. G. Denisov (Nizhny Novgorod)
V. V. Novikov (Nizhny Novgorod)
Abstract According to the Kelvin theorem, unstable conservative systems with an even degree of instability can be stabilized by means of gyroscopic forces. Usually, the gyroscopic stabilization is demonstrated for a system with two degrees of freedom or a system with 2n degrees of freedom that can be split into n independent systems. For such a system (or each of the n independent systems), one can find a certain value of the parameter characterizing the gyroscopic forces such that the system becomes stable as this value is exceeded.

In this paper, a system with four interdependent degrees of freedom is considered. This system is stabilized by the same gyroscopic forces. It turns out that the stabilization conditions in this case differ from those in the cases mentioned above: the values of the parameter characterizing the gyroscopic forces belong to a finite interval, i.e., in contrast to systems with two degrees of freedom, the range of the parameter is bounded from above.
References
1.  D. R. Merkin, Introduction to the Theory of Stability of Motion [in Russian], Nauka, Moscow, 1971.
2.  N. G. Chetaev, Stability of Motion. Studies in Analytical Mechanics [in Russian], Izd-vo AN SSSR, Moscow, 1962.
Received 01 December 2003
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