High Performance Computing of the Nonlinear Dynamics of a Basketball

Abstract

This article introduces an event–driven approach for high performance computing of the nonlinear trajectory of a basketball. The high-performance approach differs from the analytical approach of finding exact solutions to the basketball shot but that is confined to special cases, and it differs from the time-stepping approach, which only approximates the solutions to the basketball shot. This paper shows that the event-driven approach is computationally faster than the time-stepping approach while being exact – capturing the advantages of both of the traditional approaches. Faster computational speed is particularly advantageous when running millions of simulations, which is necessary when analyzing the performance of a player or of a shot. Consequently, the event-driven approach will be able to provide a deeper understanding of player and shot performance in the game of basketball. In the event-driven approach, a basketball undergoes a trajectory segment, which ends in a collision with one of a number of possible bodies. The simulation considers automatically the different possibilities and determines the true body with which the ball collided. The simulation advances from one trajectory segment to the next, each separated by a collision, until the ball finally falls to the ground. The article contains illustrative examples and provides an easy-to-use MATLAB code.