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: lixb@pku.org.cn
出处
《应用数学和力学》
EI
CSCD
北大核心
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)
关键词
类摆系统
Iagrange稳定
类梯度
第二类极限环
pendulum-like system
Lagrange stability
gradient-like behavior
limit cycles of the second kind
