二阶类摆系统的临界阻尼  

Critical Damping of the Second-Order Pendulum-Like Systems

作　　者：李鑫滨[1] 黄永念[1] 杨莹[1] 黄琳[1] 

机构地区：[1]北京大学力学与工程科学系

出　　处：《应用数学和力学》2005年第1期7-15,共9页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10272001;60334030);国家重点基础研究专项经费资助项目(G20000773)

摘　　要：　首先,分析了一具有特定非线性函数的二阶类摆系统的解的性质;进而,针对具有一般非线性形式的二阶类摆系统,利用微分方程的定性分析方法讨论了其总体性质。First, the properties of solutions of a typical second-order pendulum-like system with a specified nonlinear function were discussed. Then the case with a general form of nonlinearity is considered and its global properties were studied by using the qualitative theory of differential equations. As a result, sufficient conditions for estimating the critical damp are established, which improves the work by Leonov et al. Key words pendulum-like system - Lagrange stability - gradient-like behavior - limit cycles of the second kind Chinese Library Classification O322 2000 Mathematics Subject Classification 93D21 Contributed by HUANG Young-nian Foundation items: the National Natural Science Foundation of China (10272001, 60334030); the Special Foundation for National Key Basic Research Projects (G20000773) Biography: LI Xin-bin, Doctor, E-mail: [e-mail]

关 键 词：类摆系统 Iagrange稳定 类梯度 第二类极限环 

分 类 号：O322[理学—一般力学与力学基础]