网球拍效应(TRE)指刚体绕第二惯量主轴旋转时的不稳定现象,它作为生活中常见的现象,在物理教学中常被提及,但有关的定量实验较为缺乏. 本文中,我们在约化相空间中给出了TRE的直观解释,并利用COMSOL 软件对该现象进行了研究,研究了不同初始条件参数和刚体设置对翻转周期的影响. 我们发现“翻转耗时”对初始扰动不敏感,用它代替整个翻转周期可以减少测量和仿真模拟中误差的影响,从而在COMSOL仿真中实现了0.14%的测量误差. 此外我们利用手机进行实验,观察到了TRE且定量结果与理论预期一致. 本工作有助于学生形成关于TRE的物理图像,有助于TRE的物理教学定量实验设计.
Tennis racket effect (TRE) is a phenomenon that a rigid body’s rotation along its second inertial axis is unstable. As a physical phenomenon observable in everyday life, it is often mentioned in physical teaching.However, quantitative analysis and experiments about it still lack. In this work, a reduced phase space is introduced to give an intuitive explanation of TRE. Numerical simulations of TRE using COMSOL inspected the conditions allowing TRE and identified two modes of TREs. Simulation results of different parameters including initial angular velocities and perturbations are explained by theoretical solutions. To reduce simulation errors, the time duration of a selected portion of the flipping process that is insensitive to perturbations, instead of the complete flipping period, is measured. This method realizes a measurement error of 0.14% in COMSOL simulation. Besides, we carried out an experiment using smartphone, in which two modes of TRE, as well as a linear dependence of the reciprocal of flipping duration to the z component of the initial angular velocity, is observed and matches theoretical predictions. Our work is both beneficial to students’ understanding of TRE in physics teaching and guides the design of teaching experiments considering TRE.