PENDULUM WITH LINEAR DAMPING AND VARIABLE LENGTH

Applied Mathematics and Mechanics (English Edition) ›› 2004, Vol. 25 ›› Issue (11): 1271-1276.

PENDULUM WITH LINEAR DAMPING AND VARIABLE LENGTH

蔡建平^1,3, 杨翠红², 李怡平³

1. Department of Mathematics, Zhangzhou Teachers College, Zhangzhou, Fujian 363000, P. R. China;
2. Department of Mathematics, Central China Normal University, Wuhan 430079, P. R. China;
3. Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China

收稿日期:2003-02-27 修回日期:2004-06-28 出版日期:2004-11-18 发布日期:2004-11-18

PENDULUM WITH LINEAR DAMPING AND VARIABLE LENGTH

CAI Jian-ping^1,3, YANG Cui-hong², LI Yi-ping³

1. Department of Mathematics, Zhangzhou Teachers College, Zhangzhou, Fujian 363000, P. R. China;
2. Department of Mathematics, Central China Normal University, Wuhan 430079, P. R. China;
3. Department of Mathematics, Zhongshan University, Guangzhou 510275, P. R. China

Received:2003-02-27 Revised:2004-06-28 Online:2004-11-18 Published:2004-11-18

摘要/Abstract

摘要： The methods of multiple scales and approximate potential are used to study pendulums with linear damping and variable length. According to the order of the coefficient of friction compared with that of the slowly varying parameter of length, three different cases are discussed in details. Asymptotic analytical expressions of amplitude, frequency and solution are obtained. The method of approximate potential makes the results effective for large oscillations. A modified multiple scales method is used to get more accurate leading order approximations when the coefficient friction is not small. Comparisons are also made with numerical results to show the efficiency of the present method.

Abstract: The methods of multiple scales and approximate potential are used to study pendulums with linear damping and variable length. According to the order of the coefficient of friction compared with that of the slowly varying parameter of length, three different cases are discussed in details. Asymptotic analytical expressions of amplitude, frequency and solution are obtained. The method of approximate potential makes the results effective for large oscillations. A modified multiple scales method is used to get more accurate leading order approximations when the coefficient friction is not small. Comparisons are also made with numerical results to show the efficiency of the present method.

中图分类号:

O322

蔡建平;杨翠红;李怡平. PENDULUM WITH LINEAR DAMPING AND VARIABLE LENGTH[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(11): 1271-1276.

CAI Jian-ping;YANG Cui-hong;LI Yi-ping. PENDULUM WITH LINEAR DAMPING AND VARIABLE LENGTH[J]. Applied Mathematics and Mechanics (English Edition), 2004, 25(11): 1271-1276.

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PENDULUM WITH LINEAR DAMPING AND VARIABLE LENGTH

PENDULUM WITH LINEAR DAMPING AND VARIABLE LENGTH

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