单摆自水平位置静止开始下摆的运动状况研究  

A study on the motion of a simple pendulum swinging downward from a stationary horizontal position

作　　者：邵云 SHAO Yun(School of Electronic Engineering,Nanjing Xiaozhuang College,Nanjing 211171,China)

机构地区：[1]南京晓庄学院电子工程学院,江苏南京211171

出　　处：《高师理科学刊》2021年第3期38-42,共5页Journal of Science of Teachers＇College and University

基　　金：江苏省教育科学“十三五”规划课题(D/2020/01/55)。

摘　　要：根据常规的思维逐步推导出单摆自水平位置静止开始下摆的运动学方程,结果是一椭圆积分形式.根据该运动方程并利用MATLAB和Excel软件,作出了此单摆下摆过程中的θ~t,v~t,E_(k)~t,v~θ,E_(k)~θ曲线,并加以比较和分析.这些研究将有助于加深对椭圆积分知识,以及单摆自水平位置静止开始的下摆运动的认识.作为对比,还给出了任意摆角(≤90°)的单摆自静止开始下摆的运动学方程,并且得到单摆的周期随摆角单调增加的结论.According to the conventional thinking,deduces the kinematic equation of the simple pendulum which starts to swing downward from the stationary horizontal position.The result is an elliptic integral form.According to the kinematic equation and by using MATLAB and Excel software,makes the curves of θ~t,v~t,E_(k)~t,v~θ,E_(k)~θ in the process of the single pendulum,and compares and analyzes them.These studies will help to deepen the knowledge of elliptic integral and the motion of simple pendulum swinging downward from the stationary horizontal position.As a comparison,also gives the kinematic equation of the simple pendulum with any swing angle(≤90°),and obtains the conclusion that the period of the simple pendulum increases monotonously with the swing angle.

关 键 词：单摆 水平位置 下摆 椭圆积分 运动学方程 

分 类 号：O313.1[理学—一般力学与力学基础]