非线性奇异振子的解析逼近解  

Analytical approximate solutions of a nonlinear singular oscillator

作　　者：孙维鹏[1] 吴柏生[1] 

机构地区：[1]吉林大学数学学院力学与工程科学系,长春130012

出　　处：《振动与冲击》2009年第6期104-106,共3页Journal of Vibration and Shock

基　　金：教育部新世纪优秀人才支持计划项目

摘　　要：利用修正的牛顿-谐波平衡法建立了非线性奇异振子的解析逼近周期和周期解。通过改写控制方程和选取简单、合适的校正项对牛顿-谐波平衡法进行了修正。构造的两个解析逼近周期和周期解不仅在振幅和参数全部取值范围内有效且能快速地收敛到精确解;两个逼近周期与精确周期的百分比误差分别低于0.92%和0.09%,后者比已有结果精度高。A modified Newton-harmonic balance method was used to construct analytical approximate periods and periodic solutions of the singular oscillator for describing certain phenomena in plasma physics. The Newton-harmonic balance method was modified by rewriting the original control equation and selecting the simple and suitable correction terms. Two new analytical approximate solutions obtained are effective for the whole range of initial oscillation amplitudes and parameters, and they can rapidly converge to exact solution. The percentage errors between the exact period and the two new analytical approximate ones are lower than 0.92% and 0.09%, respectively, and the latter is more accurate than the existing results.

关 键 词：非线性奇异振子 解析逼近解 牛顿-谐波平衡法 

分 类 号：O322[理学—一般力学与力学基础]