不稳定约束系统的多角度分析  

Analyzing the system with rheonomic constraint from various perspectives

作　　者：朱仁贵[1] 黄万霞[1] ZHU Ren-gui;HUANG Wan-xia(School of Physics and Electronic Information,Anhui Normal University,Wuhu,Anhui 241002,China)

机构地区：[1]安徽师范大学物理与电子信息学院,安徽芜湖241002

出　　处：《大学物理》2024年第2期5-7,12,共4页College Physics

基　　金：安徽省高校理论物理教学团队(2020jxtd106);省级质量工程项目(2019mooc066);理论力学教学示范课项目资助。

摘　　要：不稳定约束相较于稳定约束增加了问题的复杂性,但不稳定约束问题蕴含了更多的处理手段.通过转换参考系,以及灵活选用适当形式的拉格朗日方程或能量积分,可实现多种途径求解.通过不同解法的对比,可验证教材中容易忽略的一些结论,如:理想约束不依赖于参考系的选择、理想约束力即使做实功也不影响保守系拉氏方程的适用等.通过对不稳定约束问题进行多角度分析,可以有效地提高学生对分析力学重要知识点的理解和运用能力.Compared with scleronomic constraint,rheonomic constraint brings more complication,however,it can be dealed with by more means.Through transforming the reference frame,and selecting smartly the proper form of Lagrange equation or energy integral,we can solve the rheonomic constraint problem by various ways.From the comparison among different perspectives,we can verify some results that often neglected by textbooks,such as the ideal constraint does not depend on the reference frame,and the ideal constraint force has no influence on the application conditions of the Lagrange equation for conservative system,even if it does the real work.Through analyzing the rheonomic constraint problem from various perspectives,we can promote efficiently the ability of students to comprehend and apply the important knowledge of analytical mechanics.

关 键 词：不稳定约束 拉格朗日方程 能量积分 运动微分方程 

分 类 号：O316[理学—一般力学与力学基础]