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。
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.
出处
《应用数学和力学》
EI
CSCD
北大核心
2004年第11期1163-1168,共6页
Applied Mathematics and Mechanics
关键词
单摆
多尺度法
势能逼近
慢变参数
pendulum
multiple scale method
approximate potential
slowly varying parameter
