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° 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°.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.
基金
Supported by the National Natural Science Foundation of China under Grant No 10774062
the National Science Fund for Distinguished Young Scholars(No 50925103)
the Key Project of the Ministry of Education of China(No 309027).
