钟粤文,刘姝含,孙宇飞,房毅

• 1:华东理工大学理学院

摘要(Abstract)：

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。

关键词(KeyWords)： 循环摆;渐开线;数值模拟;广义坐标;拉格朗日方程

Abstract:

Keywords:

基金项目(Foundation): 华东理工大学绿色工程基金项目资助

作者(Author): 钟粤文,刘姝含,孙宇飞,房毅

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