单摆周期公式的母函数建构  

Construction on Generating Function of Simple Pendulum Period Formula

作　　者：谭志中[1] 方靖淮[1] 

机构地区：[1]南通大学理学院,江苏南通226007

出　　处：《南通大学学报（自然科学版）》2010年第4期60-64,共5页Journal of Nantong University(Natural Science Edition)　

基　　金：江苏省教育科学十一五规划课题(D/2009/01/127)

摘　　要：利用局部常化方法得到大摆角单摆周期的一些结论,通过对诸公式的改进与整合,构建了含有3个参数的大摆角单摆周期公式的母函数.根据Matlab软件对所构造母函数的拟合研究,由母函数生成了一系列高精确度的大摆角单摆周期公式,同时得到了第一类完全椭圆积分的近似公式.通过与其它方法的误差对比表明,该方法的精度有了进一步提高.Some results of large swing angle simple pendulum period were obtained by using a partial normalization method. Through the improvement and integration of various formulae, the paper constructed a generating function for the large swing angle simple pendulum period formula with 3 parameters. The fitting of the generating function was studied by the Matlab software. A series of large swing angle simple pendulum period formulae with high accuracy were generated from the generating formula and an approximate formula of complete elliptic integral was got as well. In comparison with the errors of other methods, this normalization method has a higher accuracy.

关 键 词：单摆周期 母函数 非线性方程 局部常化方法 椭圆积分 

分 类 号：O314[理学—一般力学与力学基础]