有线性阻尼和变长度的单摆

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;

摘要: 应用多尺度法和势能逼近法研究有线性阻尼和变长度的单摆．通过摩擦因数与摆长慢变参数阶的比较，详细讨论了3种不同的情况并得到振幅、频率和解的渐近分析表达式．势能逼近法的应用使结果对大幅振动也有效．当摩擦因数不是很小时，修正的多尺度法用于得到更精确的首次近似解．与数值结果的比较表明本文的方法是有效的．
- 单摆 /
- 多尺度法 /
- 势能逼近 /
- 慢变参数
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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