Applied Mathematics and Nonlinear Sciences
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Journal

Applied Mathematics and Nonlinear Sciences


Volume
& Issue

Volume 6, Issue 2


Published
on

November 22, 2021


Pages

425-430


DOI

Article

Study on the training model of football movement trajectory drop point based on fractional differential equation

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Authors

Yuefeng Che Affiliation:
Department of Public Physical Education, Yantai Nanshan University, Humanities College Yantai, Shandong, 265706, China
and Mohammed Yousuf Abo Keir Affiliation:
Applied Science University, Al Eker, Kingdom of Bahrain


Abstract

To study the landing point of the curved football track, the dynamic differential equations of the football were derived in this paper. The air resistance moment was taken into account, and the rotation axis was no longer confined to the vertical direction. We compare various soccer movement regularity of different initial angular velocity 0, in turn, using standard numerical methods to solve differential equations, the selection of the initial angular velocity of three typical 0s has been carried on the detailed numerical study, and the results show that: in the same velocity V play football, corresponding to different initial angular velocity 0, the movement of football is an obvious difference. Conclusion: For the same V = 5 + 28 + 11 m/s, when no rotation Ω 0 = 0, the trajectory of the football is the usual trajectory of the projectile. When 0 = 2 − 2 + 16 rad/s, the trajectory of the football is a typical banana ball trajectory; When 0 = 13+0+0 rad/s, the trajectory of the football shows the phenomenon of left-right fluttering, similar to the fallen leaf ball.


Keywords

football, fractional differential equation, magnus effect, digital to analog, 34A08


Citation

Che, Y. & Abo Keir, M. Y. (2021). Study on the training model of football movement trajectory drop point based on fractional differential equation. Applied Mathematics and Nonlinear Sciences, 6(2), 425–430. https://doi.org/10.2478/amns.2021.2.00095
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