## 留言板

 引用本文: 蔡建平, 杨翠红, 李怡平. 有线性阻尼和变长度的单摆[J]. 应用数学和力学, 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.

• 中图分类号: O322

## Pendulum With Linear Damping and Variable Length

• 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．
•  [1] Nayfeh A H, Mook D T.Nonlinear Oscillations[M].New York: Wiley, 1979. [2] Bogoliubov N N, Mitropolsky Y A.Asymptotic Methods in the Theory of Nonlinear Oscillations[M]. Delhi: Hindustan Publishing Co,1961. [3] Yuste S B. On Duffing oscillators with slowly varying parameters[J].Internat J Non-Linear Mech,1991,26(5):671—677. [4] Coppola V T, Rand R H.MACSYMA program to implement averaging using elliptic functions[A].In:Meyer K R,Schmidt D S Eds.Computer Aided Proofs in Analysis[C].New York: Springer,1991,78—81. [5] LI Yi-ping. Free electron lasers with variable parameter wigglers, a strictly nonlinear oscillator with slowly varying parameters[D].Ph D Dissertation.Seattle: University of Washington,1987. [6] Kuzmak G Z. Asymptotic solutions of nonlinear second order differential equations with variable coefficients[J].Pure Math Manuscript,1959,23:515—526. [7] Kevorkian J, Cole J D.Perturbation Methods in Applied Mathematics[M].New York: Springer, 1981. [8] Kevorkian J, Li Y P. Explicit approximations for strictly nonlinear oscillators with slowly varying parameters with applications to free-electron lasers[J].Studies in Applied Mathematics,1988,78(2):111—165. [9] 李怡平.负阻尼周期运动的经过时间[J].应用数学和力学,1992,13(8):693—697.

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##### 出版历程
• 收稿日期:  2003-02-27
• 修回日期:  2004-06-28
• 刊出日期:  2004-11-15

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