| 基于恒等变换的单摆振动解析逼近 |
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| 引用本文： | 周红庆,;吕洪斌. 基于恒等变换的单摆振动解析逼近[J]. 吉林林学院学报, 2007, 0(5): 390-393 |
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| 作者姓名： | 周红庆, 吕洪斌 |
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| 作者单位： | [1]中原工学院信息商务学院,河南郑州450007; [2]北华大学数学学院,吉林吉林132033 |
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| 摘 要： | 应用修正的谐波平衡法构造了单摆大幅振动的解析逼近周期和周期解．通过引入三角变换或反三角变换将单摆振动方程恒等变形为关于新变量的Duffing方程或其他易于处理的非线性振动方程，利用牛顿谐波平衡法构造了单摆振动的解析逼近解．给出的解析逼近周期及周期解简单易用，几乎在振幅（初始摆角）的全部取值范围内，都有很高的逼近精度．
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| 关 键 词： | 单摆 解析逼近 牛顿谐波平衡法 |
Analytical Approximate for the Simple Pendulum Oscillation Based on Identical Transformation |
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| Affiliation: | ZHOU Hong-qing, LU Hong-bin ( 1. College of Information and Bussiness, Zhongyuan University of Technology, Zhengzhou 450007, China ; 2. Mathematics College of Beihua University ,Jilin 132033, China ) |
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| Abstract: | Analytical approximate period and periodic solutions of large amplitude oscillation of a simple pendulum are constructed by using harmonic balance method. First, the simple pendulum equation is transformed identically into dulling equation or other simple equations by trigonometric function or antitrigonometric function. Subsequently, the resulting equations are approximately solved by Newton harmonic balance method. The new analytical approximate period and periodic solutions show excellent agreement with the numerically exact solutions, and are valid over nearly the whole range of oscillation amplitudes. |
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| Keywords: | Simple pendulum Analytical approximate Newton harmonic balance method |
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