Accurate Period Approximation for Any Simple Pendulum Amplitude

被引：3
|
作者：
Xue De-Sheng [1 ]
Zhou Zhao [1 ]
Gao Mei-Zhen [1 ]
机构：
[1] Lanzhou Univ, Minist Educ, Key Lab Magnetism & Magnet Mat, Lanzhou 730000, Peoples R China
来源：
CHINESE PHYSICS LETTERS | 2012年 / 29卷 / 04期
基金：
中国国家自然科学基金;
关键词：
NONLINEAR PENDULUM; FORMULAS;
D O I：
10.1088/0256-307X/29/4/044601
中图分类号：
O4 [物理学];
学科分类号：
0702 ;
摘要：
Accurate approximate analytical formulae of the pendulum period composed of a few elementary functions for any amplitude are constructed. Based on an approximation of the elliptic integral, two new logarithmic formulae for large amplitude close to 180 degrees are obtained. Considering the trigonometric function modulation results from the dependence of relative error on the amplitude, we realize accurate approximation period expressions for any amplitude between 0 and 180 degrees. A relative error less than 0.02% is achieved for any amplitude. This kind of modulation is also effective for other large-amplitude logarithmic approximation expressions.
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页数：4
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