文献类型：期刊文献

中文题名：CUPT 2019循环摆研究

英文题名：RESEARCH ON CIRCULAR PENDULUM IN CUPT 2019

作者：钟粤文[1];刘姝含[1];孙宇飞[1];房毅[1]

机构：[1]华东理工大学理学院,上海200237

年份：2021

卷号：31

期号：2

起止页码：107

中文期刊名：物理与工程

外文期刊名：Physics and Engineering

收录：CSTPCD

基金：华东理工大学绿色工程基金项目资助。

语种：中文

中文关键词：循环摆;渐开线;数值模拟;广义坐标;拉格朗日方程

外文关键词：circular pendulum;involute;numerical simulation;generalized coordinates;Lagrange equation

摘要：2019年CUPT第14题“循环摆”描述了一个在生活中常见却物理原理深刻的现象。所谓循环,指的能够旋转一周以上,约定轻物体绕杆旋转一圈以上,就形成了循环摆。实验中观察循环摆的轨迹,发现其必然会过渡到渐开线。利用拉格朗日方程可得描述轻物运动的非线性常微分方程组,据此方程组分析过渡到渐开线时刻的各物理量的变化规律、确定形成循环摆的判据;同时,通过实验探究不同初始条件下对过渡到渐开线时刻的各物理量的影响,并与理论分析所得比较。结果表明,随着初始条件的改变,过渡到渐开线时:轻物绕杆角速度与轻物到杆的线长的变化趋势总是相反,且两者随着初始角度的改变必有一极值,而该极值总是在相同的初始角度下取得;轻物与水平面的夹角总与初始条件正相关。
The“circular pendulum”in question 14 of 2019 CUPT describes a phenomenon that is common in life but has profound physical principles.The so-called cycle refers to the ability to rotate more than one cycle,so it is agreed that a light object rotates more than one cycle around the rod to form a circular pendulum.Observing the trajectory of the circular pendulum in the experiment,it is found that it will inevitably transition to an involute curve.The Lagrange equation can be used to describe the nonlinear ordinary differential equations that describe the movement of light objects.According to these equations,the change law of each physical quantity at the time of transition to the involute curve is analyzed,and the criterion for forming a cyclic pendulum is determined.At the same time,through experiments,the effect of different initial conditions on the physical quantities at the time of transition to the involute is explored,and compared with the theoretical analysis.The results show that when transitioning to the involute,with the change of the initial conditions,the change trend of the angular velocity of the light object around the rod and the line length of the light object to the rod are always opposite,and the two must have an extreme value with the change of the initial angle.And the extreme value is always obtained at the same initial angle.The angle between the light object and the horizontal plane is always positively correlated with the initial conditions.