非光滑轨道约束反力问题求解及Mathematica数值计算与分析  

Solution of constraint reaction force on non-smooth orbit and numerical calculation and analysis by Mathematica software

作　　者：叶志强 郭琴 YE Zhi-qiang;GUO Qin(College of Physics and Communication Electronics,Jiangxi Normal University,Nanchang,Jiangxi 330022,China)

机构地区：[1]江西师范大学物理与通信电子学院物理系

出　　处：《大学物理》2019年第8期59-62,共4页College Physics

基　　金：江西省高等学校教学改革研究重点项目(JXJG-16-2-2)资助

摘　　要：工程设计中常常要将轨道对物体的支承力纳入到考虑范畴,而非光滑轨道最贴近物理实际,因而本文将研究约束在非光滑轨道上运动的小环所受约束反力问题.利用质点运动微分方程求出了小环在抛物线轨道任意位置处法向约束反力的解析解,研究了摩擦力对小环运动过程的影响,并借助Mathematica软件对小环前进、返回的完整过程进行了数值计算与分析.本文给出了此类问题求解的范例,所采用的求解技巧可适用于其它形状的轨道.In engineering design,the supporting force of the orbit to the object is often taken into consideration,and the non-smooth orbit is closest to the physical reality.This paper studies the constraint force problem of the small ring constrained on the non-smooth orbit.By using the differential equation of particle motion,the analytical solution of the constraint reaction of a small ring at any position on the parabolic orbit is obtained.At the same time,the effect of friction on the motion process of small ring is studied.And the numerical calculations and analysis of the complete process of forward and return movement is performed with the help of Mathematica software.The example of solving this kind of problem is given.The solution technique of the non-smooth orbit problem can be applied to other forms of orbits.

关 键 词：摩擦力 非光滑轨道 MATHEMATICA软件 约束反力 数值计算与分析 

分 类 号：O311.4[理学—一般力学与力学基础]