摘要
单摆作为一种重要的理想模型,成为力学和理论力学课程的重点教学内容.由于摆锤做曲线运动,人们常常在极坐标和自然坐标系下运用牛顿运动定律或角动量定理分析单摆动力学方程.随意假设摆锤的初始状态和规定坐标系的正向可能导致负角.然而,角度中隐藏的负号很容易被初学者忽视进而导致错误结论.适当选取示意图和坐标系正向可以避免负角从而实现快速且准确地分析出单摆动力学方程.
As an important ideal model,simple pendulum has become an important teaching content in mechanics and theoretical mechanics courses.Because of the curved motion of the pendulum,people often use Newton′s law of motion or the angular momentum theorem to analyze the dynamic equation of a single pendulum in polar coordinates and natural coordinates.Assuming the initial state of the pendulum and the positive direction of the coordinate system casually may result in a negative angle.However,this negative sign hidden in the angle is usually overlooked by beginners and leads to false conclusions.Proper selection of the diagram and the positive direction of coordinate system can avoid the negative angle,so that the dynamic equation of the pendulum can be analyzed quickly and accurately.
作者
董宝平
鲁军旺
张婷婷
郑发州
罗正鸿
DONG Baoping;LU Junwang;ZHANG Tingting;ZHENG Fazhou;LUO Zhenghong(School of Physics and Electronics,Qiannan Normal University for Nationalities,Duyun 558000,China)
出处
《高师理科学刊》
2024年第1期89-93,共5页
Journal of Science of Teachers＇College and University
基金
黔南民族师范学院教改课题(2021xjg028,2016xbkjx0808)。
关键词
角动量定理
单摆动力学方程
极坐标
自然坐标
坐标系正方向
angular momentum theorem
simple pendulum dynamic equation
polar coordinates
natural coordinates
positive direction of coordinate system
