Matlab求解理论力学问题系列(四)乒乓球的滚动  

THE ROLL OF A TABLE TENNIS

作　　者：高云峰[1] GAO Yunfeng(School of Aerospace Engineering,Tsinghua University,Beijing 100084,China)

机构地区：[1]清华大学航天航空学院,北京100084

出　　处：《力学与实践》2021年第5期753-759,共7页Mechanics in Engineering

摘　　要：本文讨论了乒乓球运动的理论解和数值解。在考虑摩擦、滚动摩阻、空气阻力等条件的一般情况下,只能获得部分解析解,而采用数值计算的方法可获得系统所有的运动规律。文章介绍了如何利用Matlab处理分段函数问题,包括求解微分代数方程、利用积分中断条件确定分段的时间点,以及利用部分解析解验证数值计算的准确性等,最后通过大量计算获得乒乓球向前运动及向后运动的分界线,以及乒乓球正好回到出发位置的条件。Theoretical and numerical solutions of the kinematics of table tennis are discussed in this paper.Under the general conditions of friction(sliding, rolling friction and air resistance), analytical solutions can be obtained only in limited conditions, but numerical solutions are universally available. This paper handles various numerical problems in solving the kinematics with Matlab, including using piecewise function,solving differential-algebraic equation, obtaining the interruption point of the integral equation, and verifying the accuracy of the numerical results through comparing with available analytical solutions. At last, two critical conditions are investigated, one for the determination of forward or backward motion of the ball, the other for the ball jumping back to the starting position.

关 键 词：微分代数方程 解析解 数值解 积分中断 

分 类 号：O313.3[理学—一般力学与力学基础]