“甲虫爬环”问题的解析

大学物理 ›› 2016, Vol. 35 ›› Issue (8): 22-24.

“甲虫爬环”问题的解析

李力1，张银2

1. 重庆清华中学，重庆400054; 2. 郑州轻工业学院数学与信息科学学院，河南郑州450002

收稿日期:2015-10-18 修回日期:2015-11-22 出版日期:2016-08-20 发布日期:2016-08-20
通讯作者: 通讯作者:张银，E-mail: agerchang@ hotmail.com
作者简介:李力( 1972—) ，男，重庆人，重庆清华中学高级教师、特级教师.

Analysis of beetle and ring problem

LI Li1，ZHANG Yin2

1. ChongqingQinghua High School，Chongqing 400054，China; 2. College of Mathematics and Information Science，Zhengzhou University of Light Industry，Zhengzhou，Henan 450002，China

Received:2015-10-18 Revised:2015-11-22 Online:2016-08-20 Published:2016-08-20

摘要/Abstract

摘要： 比较简捷、直观地运用质点系动力学解析“甲虫爬环”问题，进一步解得甲虫以及原来与甲虫相接触的圆环上“标记点”的轨迹方程，并描绘出不同质量比情况下二者的轨迹，标记点的运动轨迹是圆内旋轮线.

关键词: 甲虫爬环, 标记点, 圆内旋轮线

Abstract: The“beetle and ring problem”is analyzed tersely and intuitively by mass-point set mechanics. The equations of beetle and marked point’s track are solved. Then the movement trajectories with different quality ratio are plotted and trajectory of latter is hypocycloid.

Key words: beetle and ring problem, marked point, hypocycloid

李力，张银. “甲虫爬环”问题的解析[J]. 大学物理, 2016, 35(8): 22-24.

LI Li，ZHANG Yin. Analysis of beetle and ring problem[J]. College Physics, 2016, 35(8): 22-24.