关键词: 网球拍效应, COMSOL, 数值模拟, 约化相空间

Abstract: 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.

Key words: tennis racket effect, COMSOL, numerical simulation, reduced phase space