Pendulum With Linear Damping and Variable Length

CAI Jian-ping; YANG Cui-hong; LI Yi-ping

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Article Navigation > Applied Mathematics and Mechanics > 2004 > 25(11): 1163-1168

CAI Jian-ping, YANG Cui-hong, LI Yi-ping. Pendulum With Linear Damping and Variable Length[J]. Applied Mathematics and Mechanics, 2004, 25(11): 1163-1168.

Citation:

CAI Jian-ping, YANG Cui-hong, LI Yi-ping. Pendulum With Linear Damping and Variable Length[J]. Applied Mathematics and Mechanics, 2004, 25(11): 1163-1168.

Citation:

CAI Jian-ping, YANG Cui-hong, LI Yi-ping. Pendulum With Linear Damping and Variable Length[J]. Applied Mathematics and Mechanics, 2004, 25(11): 1163-1168.

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Pendulum With Linear Damping and Variable Length

Department of Mathematics, Zhangzhou Teachers College, Zhangzhou, Fujian 363000, P. R. China;
Department of Mathematics, Central China Normal University, Wuhan 430079, P. R. China;

Received Date: 2003-02-27
Rev Recd Date: 2004-06-28
Publish Date: 2004-11-15

Abstract

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 were discussed in details. Asymptotic analytical expressions of amplitude, frequency and solution were 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.
- pendulum,
- multiple scale method,
- approximate potential,
- slowly varying parameter

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References(9)

References

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