Study of soccer ball flight trajectory

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.