Abstract
In this paper the trajectories of a soccer ball for the most important kicks in the football game - a corner kick and a direct free kick are studied. The soccer ball is modelled as an ideal rigid hollow spherical body with six degrees of freedom, which performs a general motion in an immovable air environment with constant parameters. The ball 3D orientation is determined by the three Cardan angles. The aerodynamic forces and moments with which the air environment acts to the ball are taken into account. Two of the most dangerous areas of the football goal are defined. Differential equations which describe the motion of the soccer ball are solved numerically by MatLab-Simulink.
Highlights
Football is one of the most popular ball games
The main objectives of this paper can be formulated, as follows: - To define the most dangerous zone in the upper left or right corner of the goal, which is farthest from the goalkeeper and the ability to score is greatest; - To find the initial linear and angular velocities initial angles which are enough for soccer ball to go in the above-mentioned dangerous zone using two kind of soccer strokes; - To illustrate the trajectories of potential successful kicks graphically
The other two free kicks are directed to the left target, as they are realized with inside and outside spin
Summary
Football is one of the most popular ball games. The footballer skills to give the soccer ball the necessary direction, speed and rotation is an extremely important quality that can be improved and perfected if the physical nature of the soccer ball motion in the air is known, as well as the factors that affect this flight. In the second group of researches [15-18, etc.] the ball is considered as an immovable and it is flowed by the moving fluid environment. These studies are classical and are related to the presence of a fluid tube (tunnel). A mathematical study of the soccer ball aerodynamic interaction with the fluid environment based on the boundary layer theory is treated in details in [19, 20]. In the researches [23-26] the most important kicks in the football game /direct free kick and corner kick/ are studied. The main objectives of this paper can be formulated, as follows: - To define the most dangerous zone in the upper left or right corner of the goal, which is farthest from the goalkeeper and the ability to score is greatest; - To find the initial linear and angular velocities initial angles which are enough for soccer ball to go in the above-mentioned dangerous zone using two kind of soccer strokes; - To illustrate the trajectories of potential successful kicks graphically
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