非线性单摆周期的多尺度微扰解  

A Solution for the Period of the Nonlinear Pendulum by Multi-Scale Perturbation Method

作　　者：戴同庆[1] 程衍富[1] 

机构地区：[1]中南民族大学电子信息工程学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2009年第3期66-69,共4页Journal of South-Central University for Nationalities：Natural Science Edition

摘　　要：应用二阶多尺度微扰法研究了非线性单摆的振动周期,得到了一个大角度摆动情况下周期的近似公式.与精确的椭圆积分的级数展开对比发现,在摆角小于90度范围内两者的误差不大于1%.结果表明:多尺度微扰法是研究非线性单摆周期的一种较好的近似方法.The period of the nonlinear pendulum is studied by the second-order multi-scale perturbation method. An approximate formula of the nonlinear pendulum period is obtained for large-angle oscillation. Compared with precise result through series expansion of elliptic integrals, the error is less than 1% when the swing angle is less than 90 degree. Therefore, the multi-scale perturbation is a better approximation method for solving the period of the nonlinear pendulum.

关 键 词：单摆 多尺度微扰 周期 

分 类 号：O322[理学—一般力学与力学基础]