Dynamics of the basketball shot with application to the free throw
- 24 November 2006
- journal article
- research article
- Published by Taylor & Francis Ltd in Journal of Sports Sciences
- Vol. 24 (12), 1303-1314
- https://doi.org/10.1080/02640410500520401
Abstract
A completely general three-dimensional dynamic model is presented for the motion of basketball shots that may contact the rim, the backboard, the bridge between the rim and board, and possibly the board and the bridge simultaneously. Non-linear ordinary differential equations with six degrees of freedom describe the ball angular velocity and ball centre position. The model includes radial ball compliance and damping and contains five sub-models: purely gravitational flight, and ball – rim, ball – bridge, ball – board, and ball – bridge – board contact. Each contact sub-model has both slipping and non-slipping motions. Switching between the sub-models depends on the reaction force at, and velocity of, the contact point. Although the model can be used to study shots from any point on the court, we here use it to study the sets of free throw release angle, velocity, angular velocity, and lateral deviation angle that result in success (capture), as well as underhand free throws and those using an under-inflated ball. Free throw shots with larger backspin, lower inflation pressures, and underhand release conditions are shown to result in larger capture percentages.This publication has 10 references indexed in Scilit:
- Optimizing the Release Conditions for a Free Throw in Wheelchair BasketballJournal of Applied Biomechanics, 2004
- Dynamics of basketball-rim interactionsSports Engineering, 2004
- Numerical Analysis of the Basketball ShotJournal of Dynamic Systems, Measurement, and Control, 2003
- How to hit home runs: Optimum baseball bat swing parameters for maximum range trajectoriesAmerican Journal of Physics, 2003
- Basketball shooting strategies — the free throw, direct shot and layupSports Engineering, 2003
- Dynamics of Golf Ball-Hole Interactions: Rolling Around the RimJournal of Dynamic Systems, Measurement, and Control, 1999
- Optimal trajectory for the basketball free throwJournal of Sports Sciences, 1997
- How much air is in a basketball?American Journal of Physics, 1987
- Kinematics of the free throw in basketballAmerican Journal of Physics, 1981
- Physics of basketballAmerican Journal of Physics, 1981