| 一类非线性Jerk方程的解析逼近解 |
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| 引用本文： | 李鹏松,孙维鹏.一类非线性Jerk方程的解析逼近解[J].吉林大学学报(理学版),2007,45(2):193-196. |
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| 作者姓名： | 李鹏松 孙维鹏 |
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| 作者单位： | 1. 东北电力大学 理学院, 吉林省 吉林 132012; 2. 吉林大学 数学学院, 长春 130012 |
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| 摘 要： | 将牛顿线性化方法与谐波平衡法组合起来建立一类非线性Jerk方程周期及周期解的改进解析逼近. 在利用谐波平衡法前先将变形后的控制方程线性化, 得到线性代数方程组， 极大地简化了经典谐波平衡法的复杂性. 所给出的改进解析逼近在初始速度的允许取值范围内， 精度都较高.
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| 关 键 词： | 非线性Jerk方程 牛顿 谐波平衡法 解析逼近 |
| 文章编号： | 1671-5489(2007)02-0193-04 |
| 收稿时间： | 2006-04-30 |
| 修稿时间： | 2006年4月30日 |
Analytical Approximate Solutions to a Class of Non-linear Jerk Equations |
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| LI Peng-song,SUN Wei-peng.Analytical Approximate Solutions to a Class of Non-linear Jerk Equations[J].Journal of Jilin University: Sci Ed,2007,45(2):193-196. |
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| Authors: | LI Peng-song SUN Wei-peng |
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| Institution: | 1. College of Sciences, Northeast Dianli University, Jilin 132012, Jilin Province, China;2. College of Mathematics, Jilin University, Changchun 130012, China |
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| Abstract: | By combining the Newton method with the method of harmonic balance(HB),we have established improved analytical approximations to the period and the corresponding periodic solution to the non-linear Jerk equations.This method is established by successively linearizing the rewritten governing equation and,subsequently,appropriately imposing the HB method in order to obtain linear algebraic equations.Therefore,the complexity of the HB method has been greatly simplified.The improved solutions are in excellent agreement with the numerically exact solution,and are valid for small and large allowable values of initial velocity amplitude. |
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| Keywords: | non-linear Jerk equations Newton-harmonic balance method analytical approximation |
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