摘要
在现有文献基础上对弧线足球的研究进行了两方面的改进:考虑了空气阻力矩;足球转动轴不再局限于竖直方向.这些改进使得本文所模拟的物理条件更接近实际,而且能够比较各种不同初始角速度ω_0的足球运动规律.我们先推导出足球的动力学微分方程组,进而用标准的数值方法求解微分方程组、给出足球飞行的动画片.选择三种典型的初始角速度ω_0进行了具体的数值研究,数值结果表明:以相同的初速度V0踢出足球,对应于不同的初始角速度ω_0,足球的运动情况有明显的差别.对于相同的V0=5i+28j+11km/s,当无旋转ω_0=0时,足球的轨迹是平常的抛体运动轨迹;当ω_0=2i-2j+16krad/s时,足球的轨迹是典型的香蕉球轨迹;当ω_0=13i+0j+0krad/s时,足球的轨迹呈现出左右飘动的现象,类似于落叶球.
On the basis of the existing literature about Banana kick research, we have made two improvements： Air resistance moment is considered; Football ＇s rotation axis is no longer limited to the upright direction. So,the physical condition of the digital simulation in this paper is closer to the actual situation and the motion laws of the football in a variety of different initial angular velocity ω_0can be compared. The dynamical differential equations of the football are derived,and then are solved by using standard numerical method. The animation of the football motion is given. In this paper,the numerical study about three typical initial angular velocity ω_0was carried out. The results show that the motion of the football is obviously different with the same initial velocity V0and different ω_0. For V0= 5i ＋ 28j ＋ 11km / s,the motion trajectory is a trajectory of the usually projectile motion when ω_0= 0; the motion trajectory is a typical trajectory of banana kick when ω_0= 2i- 2j ＋16krad / s; the motion trajectory shows a left fluttering-right fluttering phenomenon（ similar to falling leaf） when ω_0= 13i ＋ 0j ＋ 0krad / s.
出处
《广东第二师范学院学报》
2016年第3期63-67,共5页
Journal of Guangdong University of Education
基金
广东省高等学校物理专业综合改革试点项目(XM060012物理学)
关键词
足球
旋转
马格努斯效应
弧线球
数字模拟
football
rotation
Magnus effect
banana kick
digital simulation
