| 形如d^2χ／dt^2＋aχ^-n＋b=0的微分方程解的研究 |
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| 引用本文： | 库少平 严鹤 胡业发 周祖德. 形如d^2χ／dt^2＋aχ^-n＋b=0的微分方程解的研究[J]. 华中科技大学学报(自然科学版), 2004, 32(11): 82-84 |
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| 作者姓名： | 库少平 严鹤 胡业发 周祖德 |
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| 作者单位： | [1]武汉理工大学计算机科学与技术学院，湖北武汉430070 [2]华中科技大学电子与信息工程系，湖北武汉430074 [3]武汉理工大学数字制造湖北省重点实验室，湖北武汉430070 |
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| 基金项目： | 国家自然科学基金资助项目(50175084);湖北省自然科学基金资助项目(2001ABA002). |
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| 摘 要： | 对于形如d^2χ／dt^2 aχ^-n b=0的二阶非线性微分方程，注意到当n=2时该方程的一个工程背景，以此工程背景为物理模型，指明在n=2时该微分方程的解X(f)是一个作周期振动的周期函数(但不是正弦函数)．以经典力学理论为基础，求出了当n=2时函数X(f)的振幅的解析表达式，并求出了周期的积分表达式，求出了做简谐振动时的振幅和周期的近似表达式．对n为任意自然数时的情形进行了推广分析，认为方程的解仍然是周期振动函数．给出了部分数值仿真结果．
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| 关 键 词： | 非线性微分方程 物理模型 周期 振幅 |
| 文章编号： | 1671-4512(2004)11-0082-03 |
| 修稿时间： | 2004-02-19 |
Solution of the differential equation as d2x/dt2+ax-n+b=0 |
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| Ku Shaoping Yan He Hu Yefa Zhou Zude Ku Shaoping Assoc. Prof., School of Computer Science and Technology,Wuhan University of Technology,Wuhan ,China.. Solution of the differential equation as d2x/dt2+ax-n+b=0[J]. JOURNAL OF HUAZHONG UNIVERSITY OF SCIENCE AND TECHNOLOGY.NATURE SCIENCE, 2004, 32(11): 82-84 |
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| Authors: | Ku Shaoping Yan He Hu Yefa Zhou Zude Ku Shaoping Assoc. Prof. School of Computer Science Technology Wuhan University of Technology Wuhan China. |
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| Affiliation: | Ku Shaoping Yan He Hu Yefa Zhou Zude Ku Shaoping Assoc. Prof., School of Computer Science and Technology,Wuhan University of Technology,Wuhan 430070,China. |
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| Abstract: | An engineering background was found in the field of electric bearing technology. According to the physical model based on the background, it was pointed out that the solution X(t) was a periodic function (not sine function). When n=2, the analytical expression of the period and the integration expression of the amplitude were derived using the classical mechanics. An approximate expression of the amplitude and the period of the simple harmonic vibration were derived. The result was analyzed when n was an arbitrary positive integer. Simulation result was presented. The analysis method and the conclusion were useful to the relative study and practice. |
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| Keywords: | non-linear differential equations physical model period amplitude |
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