Nonlinear dynamics of a basketball rolling around the rim

Antali, Mate; Havas, Vince; Hogan, S. J.; Stépàn, Gábor

doi:10.1007/s11071-021-06507-y

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…Although not visible to the eye, the ball actually undergoes rapid and repeated contact with the ring. These result coincide with those obtained analytically in [20]. Finally, we illustrate that the computer time of the event-driven approach is lower than the computer time of the time-stepping approach.…”

Section: Resultssupporting

confidence: 88%

“…For example, the nonlinear three-dimensional dynamics of a basketball rolling and slipping on the rim could now be analyzed in great detail by the time stepping approach [20]. Furthermore, it became possible to allow for any combination of ball collisions with the backboard, rim, and bridge, without knowing the combination of collisions in advance; the analysis also became all-inclusive.…”

Section: Advancement Of the State-of-the-artmentioning

confidence: 99%

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High Performance Computing of the Nonlinear Dynamics of a Basketball

Silverberg,

Tran

2023

Preprint

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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.

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Section: Resultssupporting

confidence: 88%

Section: Advancement Of the State-of-the-artmentioning

confidence: 99%

High Performance Computing of the Nonlinear Dynamics of a Basketball

Silverberg,

Tran

2023

Preprint

View full text Add to dashboard Cite

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High performance computing of the nonlinear dynamics of a basketball

Silverberg,

Tran

2024

Nonlinear Dyn

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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 timestepping 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 exactcapturing 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-touse MATLAB code.

show abstract