用数学方法研究乒乓球上旋球的飞行轨迹

通过对乒乓球的受力分析建立乒乓球的动力学模型进而建立数学模型并用数学软件Matlab进行绘图,从而揭示旋转速率对乒乓球的飞行轨迹的影响。乒乓球的上旋球是攻击技术中最常用的乒乓球技术。乒乓球在飞行过程中基本上受到四种力的作用,包括重力、飞行阻力、浮力还有马格努斯力。通过受力分析建立动力学方程用Matlab对乒乓上旋球的飞行轨迹进行绘图分析得知,乒乓球的飞行轨迹和乒乓球的旋转速率有重要关系。旋转越强的上旋球其弧线的弯曲程度越明显,第一弹跳点越近,飞行的垂直高度越低。通过对比不同的旋转速率的乒乓球的飞行轨迹发现:造成上述现象的原因是乒乓球的旋转速率不同,其又对应着不同的马格努斯力。

Dynamical model is established via force analysis of table tennis and then mathematical model is es-tablished employing mathematical software Matlab in drawing, in order to reveal the infldences of rotation speed on the night path of tennis. Topspin tennis is a tennis technique most commonly used in the attack technology. Table Tennis is basically affected by four forces in the process of the flight, including gravity, drag, buoyancy and Magnus force. Flight path of topspin tennis is drawn and analyzed through the stress analysis and dynamical equation by using Matlab. The important relationship between the rotation rate of table tennis and table tennis ball flight trajectory is revealed through the comparative analysis： The stronger the rotation of topspin is, the more obvious in the degree of arc crook, the closer the first bounce point is, and the lower the vertical height of flight. It is founded that the reason of the above phenomenon lies in the different speed of rotation and magnus force corresponding to the different speed of rotation.