用算术几何平均值法求单摆周期近似解

Approximate Solution to Period of Simple Pendulum by Using Arithmetic-Geometric Mean

采用算术几何平均值法研究了单摆周期的近似解,得出了简洁而严密的单摆周期近似解计算公式,并与其它的近似解进行了比较。结果表明:采用算术几何平均值法计算的单摆近似解比其它近似解有较高的精确度。该方法也适合其它涉及椭圆积分的物理问题的求解。

This paper is to introduce a simple and precise computational formula of approximate solution to period of simple pendulum by using arithmetic-geometric mean,and the solution has been compared with other accurate and various approximate ones.The results show that,the solution to simple pendulum form this means is more accurate than those from other methods.And this method will be also suitable for other physical problems relating to elliptic integrals.