扑克牌飞行的动力学分析

DYNAMIC ANALYSIS OF A FLYING PLAYING CARD

本文研究了第33届国际青年物理学家锦标赛(IYPT)的第17题:扑克牌的飞行稳定性问题。通过对扑克牌进行定量化抛掷实验,并对飞行过程中的扑克牌进行运动与受力分析的方法,研究影响扑克牌飞行距离和轨迹的参数。首先通过对抛掷扑克牌的过程进行分析,设计了定量化的扑克牌抛掷仪器;随后在实验中,对扑克牌的出射俯仰角、角速度、高度对其轨迹及距离的影响进行了分别验证;接着基于实验中观察到的现象以及数值仿真,对扑克牌相对于自身质心的刚体运动,以及质心相对于地面的空间运动进行了分别分析,最后得出了其运动的微分方程。

In this paper,the flight stability of playing cards,the 17th question of the 33rd International Young Physicists Championship(IYPT),is studied.Through the quantitative throwing experiment of playing cards and the analysis of the movement and force of playing cards in the process of flight,the parameters affecting the flying distance and trajectory of playing cards are studied.First of all,through the analysis of the process of playing card throwing,a quantitative playing card throwing instrument is designed.Then,in the experiment,the effects of the pitch angle,angular velocity and height of the playing card on its trajectory and distance are verified respectively.Then,based on the phenomena observed in the experiment and numerical simulation,the rigid motion of the playing card relative to its own center of mass and the center of mass are analyzed.The space motion relative to the ground is analyzed respectively,and the differential equation of the motion is obtained.