On the Instability of Equilibrium of Nonholonomic Systems With Dissipation and Circulatory Forces

M. Vesković; V. Čović; A. Obradović

doi:10.3879/j.issn.1000-0887.2011.02.008

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M. Vesković, V. Čović, A. Obradović. On the Instability of Equilibrium of Nonholonomic Systems With Dissipation and Circulatory Forces[J]. Applied Mathematics and Mechanics, 2011, 32(2): 202-212. doi: 10.3879/j.issn.1000-0887.2011.02.008

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On the Instability of Equilibrium of Nonholonomic Systems With Dissipation and Circulatory Forces

doi: 10.3879/j.issn.1000-0887.2011.02.008

1.
University of Kragujevac, Faculty of Mechanical Engineering, Dositejeva 19, 36000 Kraljevo, Serbia;

Received Date: 2010-09-21
Rev Recd Date: 2010-11-04
Publish Date: 2011-02-15

Abstract

Abstract

The equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative,conservative,circulatory forces was discussed. The applied methodology was based on the existence of solutions of differential equations of motion which asymptotically tend to the equilibrium state of the system,as t→-∞. It was assumed that the kinetic energy,the Rayleigh dissipation function,the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions. The results obtained,which partially generalize results from[V V Kozlov. On the asymptotic motions of systems with dissipation. Prikl Math Mekh,1994,58 (4):31-36. (in Russian);D R Merkin. Introduction to the Theory of the Stability of Motion. 1987,Moscow:Nauka. (in Russian);W Thomson,P Tait. Treatise on Natural Philosophy. Part Ⅰ. Cambridge University Press,1879],are illustrated by an example.
- nonholonomic constraint,
- instability,
- potential,
- dissipative forces

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References(25)

References

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