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应用局部常化思想将三角函数的万能公式局部常化,得到7个新的大摆角单摆周期近似公式.利用曲线拟合的方法确定待定常数,并给出第一类完全椭圆积分的一种简洁的近似公式.将所得周期近似公式及已有近似公式的相对误差进行对比,结果表明所得单摆周期近似公式均具有很高的精度,其中的一个公式具有简洁、高精度、较实用等优点.
Abstract：Applying the thought of the variable being partly fixed to making the trigonometric universal formula to be constant in part,seven new large angle simple pendulum period formulas were obtained,a series of pending constant were confirmed by using Matlab software to curve fitting,at the same time a concise approximate formula of the first complete elliptic integral was generated.The accuracy of the relative error on the simple pendulum period formula are compare and contrast,it is sure that seven simple pendulum period formulas are all of high accuracy,and points out the virtue of one of the formulas which is concise,high precision and good practical value.
[1]刘式适,刘式达.物理学中的非线性方程[M].北京:北京大学出版社,2000:178-186.
[2]陆同兴.非线性物理概论[M].合肥:中国科学技术大学出版社,2002:266-269.
[3]赵凯华.从单摆到混沌[J].现代物理知识,1993,5(5):25-28.
[4]谭志中.求大摆角单摆周期近似解的“局部常化”方法[J].大学物理,2005,24(12):14-17.
[5]谭志中,罗礼进.用局部常化三倍角公式研究单摆周期[J].大学物理,2007,26(11):25-28.
[6]于凤军,景义林.一个单摆周期近似公式[J].大学物理,2007,26(5):18-19.
[7]袁庆新,曾凡光.对《一个单摆周期近似公式》一文的讨论[J].大学物理,2008,27(9):16-18.
[8]鞠衍清,张风雷.基于MATLAB的单摆周期近似解的比较[J].大学物理,2007,26(3):6-9.
[9]谭志中,方靖淮.单摆周期公式的母函数建构[J].南通大学学报:自然科学版,2010,9(4):60-64.
[10]薛德胜,周钊,高美珍.单摆近似周期的新形式及构造分析[J].大学物理,2010,29(8):25-28.
[11]孙秋普,闫廷刚.计算单摆周期的一种近似方法[J].齐齐哈尔大学学报:自然科学版,2009,25(2):69-72.
[12]Beléndez A,Hern觃ndez A,Beléndez T,et al.An impro-ved‘heuristic’approximation for the period of a nonlinearpendulum:linear analysis of a classical nonlinear problem[J].International Journal of Nonlinear Sciences and Num-erical Simulation,2007,8(3):329-334.
[13]Amore P,Valdovinos M C,Ornelas G,et al.The non-linear pendulum:formulas for the large amplitude period[J].Revista Mexicana De Fisica E,2007,53(1):106-111.
[14]Cromer A.Many oscillations of a rigid rod[J].AmericanJournal of Physics,1995,63(2):112-121.
[15]Hite G E.Approximations for the period of a simple pen-dulum[J].The Physics Teacher,2005,43(1):290-292.
[16]Beléndez A,Rodes J J,Beléndez T,et al.Appro-ximationfor a large-angle simple pendulum period[J].EuropeanJournal of Physics,2009,30(2):25-28.
[17]Ganley W P.Simple pendulum approximation[J].AmericanJournal of Physics,1985,53(1):73-76.
[18]Parwani R R.An approximate expression for the large an-gle period of a simple pendulum[J].European Journal ofPhysics,2004,25(1):37-39.
[19]Kidd R B,Fogg S L.A simple formula for the large anglependulum period[J].The Physics Teacher,2002,40(2):81-83.
[20]Lima F M S,Arun P.An accurate formula for the period ofa simple pendulum oscillating beyond the small angle rgime[J].American Journal of Physics,2006,74(10):892-895.
[21]Yuan Qingxing,Ding Pei.Comment on‘Approximation fora large-angle simple pendulum period[J].European Jour-nal of Physics,2009,30(5):79-80.
基本信息:
DOI：
中图分类号:O314;O171
引用信息:
[1]谭志中,杨建华.局部常化三角函数的万能公式研究单摆周期[J],2013,12(02):90-94.
基金信息:
江苏省教育厅“物理学”特色专业建设点、江苏省“十二五”高等学校重点专业建设资助项目;; 南通大学自然科学基金项目(11Z054);; 南通大学教学研究项目(2011B06)