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Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces

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Abstract

The paper discusses the equilibrium instability problem of the scleronomic nonholonomic systems acted upon by dissipative, conservative, and circulatory forces. The method is based on the existence of solutions to the differential equations of the motion which asymptotically tends to the equilibrium state of the system as t tends to negative infinity. It is assumed that the kinetic energy, the Rayleigh dissipation function, and the positional forces in the neighborhood of the equilibrium position are infinitely differentiable functions. The results obtained here are partially generalized the results obtained by Kozlov et al. (Kozlov, V. V. The asymptotic motions of systems with dissipation. Journal of Applied Mathematics and Mechanics, 58^(5), 787–792 (1994). Merkin, D. R. Introduction to the Theory of the Stability of Motion (in Russian), Nauka, Moscow (1987). Thomson, W. and Tait, P. Treatise on Natural Philosophy, Part I, Cambridge University Press, Cambridge (1879)). The results are illustrated by an example.

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Authors and Affiliations

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

    M. Vesković

  2. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade, 11000, Serbia

    V. Čović & A. Obradović

Authors
  1. M. Vesković
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  2. V. Čović
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  3. A. Obradović
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Correspondence to M. Vesković.

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Project supported by the Ministry of Science and Technological Development of the Republic of Serbia (Nos.ON174016 and TR35006)

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Vesković, M., Čović, V. & Obradović, A. Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces. Appl. Math. Mech.-Engl. Ed. 32, 211–222 (2011). https://doi.org/10.1007/s10483-011-1407-9

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  • DOI: https://doi.org/10.1007/s10483-011-1407-9

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2010 Mathematics Subject Classification

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