PENDULUM WITH LINEAR DAMPING AND VARIABLE LENGTH  

作　　者：蔡建平 杨翠红 李怡平 

机构地区：[1]Department of Mathematics, Zhangzhou Teachers College, Zhangzhou, Fujian 363000, P.R.China [2]Department of Mathematics, Zhongshan University, Guangzhou 510275, P.R.China [3]Department of Mathematics, Central China Normal University, Wuhan 430079, P.R.China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2004年第11期1271-1276,共6页应用数学和力学（英文版）

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.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.

关 键 词：PENDULUM multiple scale method approximate potential slowly varying parameter 

分 类 号：O321[理学—一般力学与力学基础]