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

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.

Generalized k-Fractional Integral Operators Associated with Pólya-Szegö and Chebyshev Types Inequalities

“…A large number of fractional integral inequalities due to different types of fractional integral operators have been established (see [10,14,19,[22][23][24][25][26][27][28][29] and references therein). Applications of fractional integral operators in differential equations and other fields can be found in [25,[30][31][32][33][34][35]. The first formulation of fractional integral operator is the Riemann-Liouville fractional integral operator, defined as follows:…”

Analysis of mechanical principle of banana ball

“…Zhao [3] analyzes forces during flight and establishes equations of motion. Che [4] visualizes the numerical solution of the equation. However, none of these research makes analysis on the whole process of the banana ball.…”

Research on intelligent soccer teaching and training model integrating virtual reality technology

“…Second, traditional training equipment is limited by the venue, climate, and other factors and cannot provide all-weather, full-scene, and all-around training. Finally, traditional teaching methods also have some problems with the degree of motivation of students [6].…”