非完整系统有耗散和循环力时的平衡不稳定性

M·韦仕科尉克; V·科尉克; A·奥布拉德尉克

doi:10.3879/j.issn.1000-0887.2011.02.008

非完整系统有耗散和循环力时的平衡不稳定性

doi: 10.3879/j.issn.1000-0887.2011.02.008

克拉古涅瓦茨大学机械工程学院,克拉列沃 36000,塞尔维亚;2.贝尔格莱德大学机械工程学院,贝尔格莱德 11000,塞尔维亚

基金项目: 塞尔维亚科技发展部出版基金资助项目(ON174016;TR35006)

详细信息

中图分类号: O316
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出版历程
- 收稿日期: 2010-09-21
- 修回日期: 2010-11-04
- 刊出日期: 2011-02-15

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

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

摘要

摘要: 讨论定常非完整系统在耗散、保守、循环力作用下的不稳定平衡问题．应用方法是基于运动微分方程解的存在性，当t→-∞时，系统渐近地趋于平衡状态．假定在平衡位置附近，动能、Reyleigh耗散函数、位置力都是无限可微函数．结果将通过一个实例说明．部分结果参见Kozlov V V. On the asymptotic motions of systems with dissipation. Prikl Math Mekh, 1994, 58(4): 31-36. (in Russian); Merkin D R. Introduction to the Theory of the Stability of Motion. Moscow: Nauka, 1987. (in Russian); Thomson W, Tait P. Treatise on Natural Philosophy, Part Ⅰ. Cambridge: Cambridge University Press, 1879．
- 非完整 /
- 不稳定性 /
- 势能 /
- 耗散力
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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参考文献(25)

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