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力学与实践 ›› 2009, Vol. 31 ›› Issue (3): 76-77.doi: 10.6052/1000-0992-2007-539

• 教育研究 • 上一篇    下一篇

圆柱体在圆弧形凹槽内作纯滚动的运动分析

王树平 李彩娟 崔红娜 吕国 代长明   

  1. 河北建筑工程学院数理系
  • 收稿日期:2007-12-03 修回日期:2008-02-18 出版日期:2009-06-08 发布日期:2009-06-08

Analysis of completely rolling of a circular column in a free circular concave trough

  • Received:2007-12-03 Revised:2008-02-18 Online:2009-06-08 Published:2009-06-08

摘要: 对在光滑水平面上可自由移动的圆弧形凹槽内作纯滚动的圆柱体的运动进行了分析,给出了 圆柱体的质心及其边缘上任意一点在静止参考系中的运动轨迹方程和圆柱体严格等时摆动的 条件,并绘出了它们相应的轨迹. 求出了圆柱体在槽内作纯滚动的运动周期,并与圆柱体被 简化为质点时的周期作了比较.

关键词: 纯滚动, 严格等时性, 周期, 运动轨迹

Abstract: A circular column,s completely rolling in a free circular concave trough on a smooth horizontal plane is investigated.the track equation of the circular column,s mass center and any point on the circular column,s edge in inertial frame of reference is deduced, the strict isochronism vibration condition is given,and the tracks is sketched by a computer; the period of vibration when the circular column is completely rolling is calculated,and the period of vibration when the circular column is completely rolling to when the circular column is completely glide are compared.

Key words: completely roll, strict isochronism, period, kinetic track