Trajectories reconstruction of spinning baseball pitches by three-point-based algorithm

摘要

In this work, a method to reconstruct trajectories by obtaining the initial conditions, velocity and angular velocity, from spinning throws is designed. It is based on considering Magnus effect can be separated from rest of forces that define the dynamics of the ball, such assumption is supported by an energetic analysis. Thus, the methodology consists in solving the two-point boundary value problem (BVP) of the movement equations without Magnus force and then adding its effect.We found that only three points (ball positions as functions of time) of a trajectory are necessary to characterize it, and consequently to solve the three-point BVP. This result is applied in an algorithm based on the shooting method, which obtains the initial conditions of synthetic trajectories by minimizing the distance between points of the original trajectory and those of the proposed trajectory, with high accuracy in a short time.