单摆问题的一种数学处理

在工程计算中，单摆的周期通常都是由近似公式Ｔ＝２πｌｇ计算而得。但此公式只能在精度要求不是很高，并且摆角很小（通常小于５°）的情况下能够得出较满意的结果。当精确度要求较高时，以及摆角较大时就会产生很大的误差。运用数学手段讨论此问题，以期大大提高其精确度，并给出相应的计算公式。

A Mathematics Treatment to Single Pendulum Problem

In engineering calculation,a period of single pendulum is usually calculated according to the approximate formula T=2 l g on the condition that accuracy need not be strictly cortrained and pendulum angle is small (usually less than five degrees),and quite satisfactory effect can be obtained.But on the contrary,when accuracy need be strictly constrained and pendulum angle is adeguately big,serious error will be risen.This paper discusses the problem by means of mathematics method in order to raise the accuracy and enlarge their application range.In the maintime,corresponding approximate formulae are given.