摘要
Kozlov将Liapunov第一方法推广到非线性力学系统,用来研究保守力和耗散力场中,运动力学系统平衡位置的不稳定性.在平衡位置分析惯性张量的异常,或者Rayleigh耗散函数系数矩阵的异常.在稳定性分析中,实际上不可能应用Liapunov逼近法,因为平衡位置的存在条件,和运动微分方程解的唯一性条件,均无法得到满足.Kozlov的广义Liapunov第一方法,不仅适用上面提及的条件,此外,还知道同样的代数表达式得到满足.给出了3个关于平衡位置的不稳定性定理.用一个例子,举例说明了得到的结果.
Liapunov＇ s first method, extended by V. Kozlov to nonlinear mechanical systems, was applied to the study of the instability of the position of equilibrium of a mechanical system moving in the field of conservative and dissipative forces. The cases with the tensor of inertia or the matrix of coefficients of the Rayleigh dissipative traction singular in the equilibrium position were analyzed. This fact renders impossible the application of Liapunov＇ s approach in the anal- ysis of stability because in the equilibrium position the conditions of existence and uniqueness of solutions of differential equations of motion were not flflfilled. It was shown that Kozlov＇ s generalization of Liapunov＇ s first method was also applied in mentioned cases on condition that besides known one algebraic expression more was fulfilled. Three theorems on the instability of the equilibrium position were formulated. The results were illustrated by an example.
出处
《应用数学和力学》
CSCD
北大核心
2011年第9期1127-1138,共12页
Applied Mathematics and Mechanics
基金
塞尔维亚共和国科学和技术发展部基金资助项目(ON174004
ON174016
TR335006)
关键词
不稳定性
异常情况
渐近运动
有势力
耗散力
instability
singular case
asymptotic motion
potential
dissipative force
