›› 2014, Vol. 36 ›› Issue (4): 486-490.DOI: 10.6052/1000-0879-13-297

• 应用研究 • 上一篇    下一篇

物体沿绳索无摩擦下滑运动研究

黄瑞璞, 卓新   

  1. 浙江大学建筑工程学院, 杭州310058
  • 收稿日期:2013-07-16 修回日期:2013-09-25 出版日期:2014-08-08 发布日期:2014-11-13
  • 通讯作者: 卓新,男,副教授.E-mail:zhuoxin@zju.edu.cn

THE FRICTIONLESS SLIDING OF AN OBJECT ALONG A ROPE

HUANG Ruipu, ZHUO Xin   

  1. College of Civil Engineering and Architecture, Zhejiang University, Hangzhou 310058, China
  • Received:2013-07-16 Revised:2013-09-25 Online:2014-08-08 Published:2014-11-13

摘要: 提出了物体在无摩擦情况下沿一段柔性绳索下滑运动力学问题的分析方法,利用牛顿第二定律建立耦合运动方程组,采用龙格-库塔(Runge-Kutta)方法编写程序对已建方程组进行求解,用Matlab 中的曲线拟合命令对方程组的数值解进行公式拟合,用得到的物体运动公式结合耦合运动方程组可求出物体下滑各时段绳索的内力. 提出的分析方法对物体在不同初始状态下的计算结果表明:绳索内力随物体的简谐振动呈周期性变化;物体下滑高度越高,经过相同位置时速度、加速度和绳索内力就越大.

关键词: 物体沿绳索下滑运动|无摩擦|力学分析

Abstract: A new method is proposed to analyze the internal force in a rope in the process of an object sliding along it without friction. A set of equations for the coupled motion is established on the basis of Newton's second law. Then, it is solved numerically by using the Runge-Kutta method, and the results are fitted through the Matlab software to obtain the formulas of motion. With the combination of the fitted formulas and the equations of motion, the internal force in the rope, as the object sliding along, is determined. Under different initial states of the object, the results, analyzed by the proposed new method, show that the internal force in the rope changes periodically in accordance with the simple harmonic motion of the object. The higher the object is released, the larger velocity and acceleration it achieves when passing through the same point on the rope, so does the internal force in the rope.

Key words: objects sliding along the rope|frictionless|mechanical analysis

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