Abstract

Matlab numerical simulation-based tennis drop point judgment model research

Author(s): Yunling Deng

In tennis competition “Hawk-Eye” actually is capturing three-dimensional coordinate, speed size, direction when tennis is flying, calculating its flight trajectory and defining its drop points. According to “Hawk-Eye” principle, the paper firstly assumes it’s breezeless and has even air density, tennis generated deformation by hitting is ignored, it accurately makes tennis flight suffered gravity, air resistance, decomposes tennis movements into vertical direction and horizontal direction, utilizes calculus thought to solve, and then gets tennis shooting range, dropping time and dropping position. Finally it increases tennis rotation, according to Bernoulli conservation formula, pressure generated Magnus force that is vertical to speed direction and angular speed direction, applies integral principle to solve Magnus force coefficient, by calculating vertical direction’s tennis rising height required time, it establishes mathematical model and detailed describes flight trajectory and drop point in case tennis is rotating, and utilizes Matlab software to draw intuitional flight trajectory graph.