摘要
任意摆幅的摆类振动由于涉及椭圆积分,问题的讨论带来一定的困难,通常仅局限于讨论摆角较小时的情况,近似处理为简谐振动.如果不做这种近似处理,对任意的摆幅,摆类的振动规律又如何,振动又有什么特点,是否是简谐振动,这是大学力学教学中学生感到困惑的问题.运用椭圆积分的理论给出了问题的解,并进行了系统、深入的讨论.
Because vibrations of pendulums for arbitrary amplitudes of the angle involve the elliptic integrals,it is difficult to investigate and solve this problem. Usually,the vibration of the ampli- tude of the angle being smaller is only discussed,which is approximated as a simple harmonic vi- bration. This paper investigates the problem which makes students feel confused in mechanics teaching and presents the angular displacement function and the period function of pendulums for arbitrary amplitudes of the angle by using the theory of elliptic integrals and the analytic method.
出处
《云南师范大学学报（自然科学版）》
2015年第3期51-55,共5页
Journal of Yunnan Normal University:Natural Sciences Edition
关键词
任意摆幅
摆类
振动
规律
Rbitrary amplitudes of the angle
Pendulums
Vibrations
Law
