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Applied Mathematics and Mechanics (English Edition) ›› 2011, Vol. 2 ›› Issue (32): 211-222.doi: https://doi.org/10.1007/s10483-011-1407-9

• Articles • 上一篇    下一篇

Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces

 M.VESKOVIC1, V.COVIC2, A.OBRADOVIC2   

  1. 1. Faculty of Mechanical Engineering, University of Kragujevac, Dositejeva 19, Kraljevo 36000, Serbia;
    2. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade 11000, Serbia
  • 收稿日期:2010-09-17 修回日期:2010-10-23 出版日期:2011-01-24 发布日期:2011-01-24

Instability of equilibrium of nonholonomic systems with dissipation and circulatory forces

 M.VESKOVIC1, V.COVIC2, A.OBRADOVIC2   

  1. 1. Faculty of Mechanical Engineering, University of Kragujevac, Dositejeva 19, Kraljevo 36000, Serbia;
    2. Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, Belgrade 11000, Serbia
  • Received:2010-09-17 Revised:2010-10-23 Online:2011-01-24 Published:2011-01-24

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2

摘要： 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.

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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