On the Instability of Equilibrium of Nonholonomic Systems With Dissipation and Circulatory Forces
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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.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.
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Key words:
- nonholonomic constraint /
- instability /
- potential /
- dissipative forces
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