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| 二阶类摆系统的临界阻尼 | |
| 引用本文： | 李鑫滨,黄永念,杨莹,黄琳. 二阶类摆系统的临界阻尼[J]. 应用数学和力学, 2005, 26(1): 7-15 |
| 作者姓名： | 李鑫滨 黄永念 杨莹 黄琳 |
| 作者单位： | 北京大学 力学与工程科学系,北京 100871;2.燕山大学 电气工程学院,秦皇岛 066004 |
| 基金项目： | 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，并由此给出了估算其临界阻尼的充分性条件．改进了Leonov等人的工作． |
| 关 键 词： | 类摆系统 Lagrange稳定 类梯度 第二类极限环 |
| 文章编号： | 1000-0887(2005)01-0007-09 |
| 收稿时间： | 2003-11-15 |
Critical Damping of the Second-Order Pendulum-Like Systems |
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| LI Xin-bin. Critical Damping of the Second-Order Pendulum-Like Systems[J]. Applied Mathematics and Mechanics, 2005, 26(1): 7-15 | |
| Authors: | LI Xin-bin |
| Affiliation: | Department of Mechanics and Engineering Science, Peking Univeristy, Beijing 100871, P. R. China; |
| Abstract: | First,the properties of solutions of a typical second-order pendulum-like system with a specified nonlinear function were dicussed.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. |
| Keywords: | pendulum-like system Lagrange stability gradient-like behavior limit cycles of the second kind |
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