一类非线性Jerk方程的解析逼近解

一类非线性Jerk方程的解析逼近解

李鹏松¹, 孙维鹏²

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

收稿日期:2006-04-30 修回日期:1900-01-01 出版日期:2007-03-26 发布日期:2007-03-26
通讯作者: 孙维鹏

Analytical Approximate Solutions to a Class of Nonlinear Jerk Equations

LI Pengsong¹, SUN Weipeng²

1. College of Sciences, Northeast Dianli University, Jilin 132012, Jilin Province, China;2. College of Mathematics, Jilin University, Changchun 130012, China

Received:2006-04-30 Revised:1900-01-01 Online:2007-03-26 Published:2007-03-26
Contact: SUN Weipeng

摘要/Abstract

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.

关键词: 非线性Jerk方程, 牛顿谐波平衡法, 解析逼近

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.

Key words: nonlinear Jerk equations, Newtonharmonic balance method, analytical approximation

中图分类号:

O322

李鹏松, 孙维鹏. 一类非线性Jerk方程的解析逼近解[J]. J4, 2007, 45(02): 193-196.

LI Pengsong, SUN Weipeng. Analytical Approximate Solutions to a Class of Nonlinear Jerk Equations[J]. J4, 2007, 45(02): 193-196.

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