大学物理 ›› 2022, Vol. 41 ›› Issue (6): 69-.doi: 10.16854/j.cnki.1000-0712.210488

• 大学生园地 • 上一篇    下一篇

圆环在抛物面上运动模式的分析与探讨

凌一凡 ,刘阳,刘玉洁,卢礼萍   

  1. 1.南京农业大学理学院,江苏南京 210095;2.南京农业大学金融学院,江苏南京 210095
  • 收稿日期:2021-09-22 修回日期:2021-11-13 出版日期:2022-06-15 发布日期:2022-06-15
  • 通讯作者: 卢礼萍,Email:lplu0227@ njau.edu.can
  • 作者简介:凌一凡 ( 2001—),男,江苏省徐州市人,南京农业大学 2019级本科生.

Analysis and discussion on the rolling motion of rings on a paraboloid

LING Yi-fan1,LIU Yang2,LIU Yu-jie1,LU Li-ping1   

  1. 1.College of Sciences,Nanjing Agricultural University,Nanjing,Jiangsu 210095,China; 2.College of Finance,Nanjing Agricultural University,Nanjing,Jiangsu 210095,China
  • Received:2021-09-22 Revised:2021-11-13 Online:2022-06-15 Published:2022-06-15

摘要: 圆环在抛物面上的运动是一种错综复杂的刚体运动,涉及许多晦涩难懂的理论知识.本文首先在实验上呈现了圆环在抛物面上的运动,获得了不同初速度方向时圆环的运动模式,即直线型、三叶草型和螺旋型.通过运动模式构造了在 xy平面内的衰减位移方程,较好的拟合了利用 Tracker软件跟踪圆环获取的实验运动轨迹,并解释了初始速度方向与圆环运动模式之间的内在关联.最后,在纯滚动理论框架内,探讨了特殊运动模式下圆环的角速度.

关键词: 抛物面 , 圆环, 刚体, 角速度

Abstract: The motion of a ring on a paraboloid is a complex rigid body motion,which involves many obscuretheoretical knowledges. In this paper,an experiment of the motion of rings on a paraboloid is presented,and the motion modes of rings in different initial velocity directions are obtained,such as linear mode,clover mode,helicalmode. On the basis of fitting the constructed motion equation to the experimental data obtained by tracker software, the relationship between motion modes and the initial direction of velocity of rings isanalyzed. In the frame of rigid body motion theory,the angular velocity of the ring of special motional modes is discussed

Key words: paraboloid, ring, rigid body, angular velocity