| 解非线性振动方程的两种摄动法的比较 |
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| 引用本文： | 周红庆,;高福顺.解非线性振动方程的两种摄动法的比较[J].吉林林学院学报,2007(6):488-492. |
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| 作者姓名： | 周红庆 ;高福顺 |
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| 作者单位： | [1]中原工学院信息商务学院,河南郑州450007; [2]北华大学数学学院,吉林吉林132033 |
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| 摘 要： | 首先介绍了解非线性振动方程的L-P摄动法和Krylov展开法,然后对两种方法进行了比较.比较可知,对恢复力是位移奇函数的单自由度保守振动系统Krylov展开法适用范围比L-P摄动法广泛;对恢复力是位移一般函数的单自由度保守振动系统两者都仅适用于弱非线性系统.两个典型例子验证了结论的正确性.
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| 关 键 词： | 摄动法 奇非线性振动系统 一般非线性振动系统 |
Comparison of Two Perturbation Methods for Nonlinear Oscillation Equations |
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| Institution: | ZHOU Hong-qing, GAO Fu-shun (1. College o3c Information and Bussiness , Zhongyuan University of Technology, Zhengzhou 450007, China ; 2. Mathematics College of Beihua University ,Jilin 132033, China ) |
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| Abstract: | The L-P perturbation method and Krylov method are reviewed firstly, and then the comparison between them is completed. For the odd nonlinear oscillation systems, the Krylov method is better than L-P perturbation method. On the other hand, for the case of general nonlinear oscillation systems, both L-P perturbation method and Krylov method are only valid for small amplitude. Two typical example＇s confirm that the conclusion presented in this paper is correct. |
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| Keywords: | Perturbation methods Odd nonlinear oscillation systems General nonlinear oscillation systems |
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