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The Ziegler effect in a non-conservative mechanical system. (English. Russian original) Zbl 1272.70081

J. Appl. Math. Mech. 74, No. 1, 51-60 (2010); translation from Prikl. Mat. Mekh. 74, No. 1, 74-88 (2010).
Summary: The destabilization of the stable equilibrium of a non-conservative system under the action of an infinitesimal linear viscous friction force is considered. In the case of low friction, the necessary and sufficient conditions for stability of a system with several degrees of freedom and, as a consequence, the conditions for the existence of the destabilization effect (Ziegler’s effect) are obtained. Criteria for the stability of the equilibrium of a system with two degrees of freedom, in which the friction forces take arbitrary values, are constructed. The results of the investigation are applied to the problem of the stability of a two-link mechanism on a plane, and the stability regions and Ziegler’s areas are constructed in the parameoter space of the problem.

MSC:

70J25 Stability for problems in linear vibration theory
70F20 Holonomic systems related to the dynamics of a system of particles
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References:

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