<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</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.

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

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

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...

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

Publié en ligne: 22 nov. 2021

Pages: 425 - 430

Reçu: 17 juin 2021

Accepté: 24 sept. 2021

DOI: https://doi.org/10.2478/amns.2021.2.00095

Mots clés
football, fractional differential equation, magnus effect, digital to analog

© 2021 Yuefeng Che et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

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

Publié en ligne: 22 nov. 2021

Pages: 425 - 430

Reçu: 17 juin 2021

Accepté: 24 sept. 2021

DOI: https://doi.org/10.2478/amns.2021.2.00095

Mots clésfootball, fractional differential equation, magnus effect, digital to analog

© 2021 Yuefeng Che et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
football, fractional differential equation, magnus effect, digital to analog