羽毛球极限挥拍速度与Fourier级数展开

Ultimate Swing Speed of Badminton and Fourier Series Expansion

为帮助羽毛球爱好者迅速提高挥拍技巧以及有效分析专业运动员的极限挥拍速度,基于实数域和复数域的傅里叶级数展开以及FFT(快速傅里叶变换)算法建立了理论向量模型。通过高阶求导计算,得到了羽毛球的理论极限挥拍速度。同时从理论上证明一般结论:击球速度在各关节运动方向一致时达到极大值,一般阶梯函数展开的极值点存在,且在斜率极大值处唯一取得。从而揭示了傅里叶级数在实数域和复数域之间的部分联系。此外,利用OpenPose人体姿态识别技术分析视频,建立实际向量模型,计算了羽毛球爱好者和专业运动员的实际速度,并将其与理论极限速度进行了对比,得出专业运动员相比羽毛球爱好者更贴近理论极限模型的结论。通过该结论验证此前理论模型的正确性,若羽毛球爱好者的挥拍动作更贴合理论极限模型,则更能达到极限速度,进而提升球技。

In order to help badminton enthusiasts to rapidly improve their swinging skills and effectively analyze the ultimate swing speed of professional athletes,a theoretical vector model is established based on the Fourier series expansion in the real number field or complex number field and the FFT(Fast Fourier transform)algorithm,and the theoretical ultimate swing speed of badminton is obtained by the high-order derivative calculation.At the same time,theoretically,the general conclusion is proved that"the swing speed reaches a maximum when the direction of movement of each joint is consistent,and that the extreme point of the general step function expansion exists and is only obtained at the slope maximum",thus revealing the partial connection of the Fourier series between the real number field and the complex number field.In addition,OpenPose human posture recognition technology is used to analyze the video,the actual vector model is established,the actual speed of badminton enthusiasts and professional athletes is calculated and compared with the theoretical ultimate speed,and it is conclude that professional athletes are closer to the theoretical ultimate model than badminton enthusiasts.The correctness of the previous theoretical model is verified through this conclusion,and it is suggested that if the swing of badminton enthusiasts is more closely to the theoretical ultimate model,they are more able to reach the ultimate speed and then improve their skills.