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TECHNICAL PAPERS

Dynamics of a Basketball Rolling Around the Rim

[+] Author and Article Information
C. Q. Liu

 DaimlerChrysler Corporation, 800 Chrysler Drive East, Auburn Hills, MI 48326-2757

Fang Li

Mechanical, Industrial and Nuclear Engineering,  University of Cincinnati, Cincinnati, OH 45221-0072

R. L. Huston1

Mechanical, Industrial and Nuclear Engineering,  University of Cincinnati, Cincinnati, OH 45221-0072

1

Corresponding author.

J. Dyn. Sys., Meas., Control 128(2), 359-364 (May 19, 2005) (6 pages) doi:10.1115/1.2194073 History: Received July 27, 2003; Revised May 19, 2005

Governing dynamical equations of motion for a basketball rolling on the rim of a basket are developed and presented. These equations form a system of five first-order, ordinary differential equations. Given suitable initial conditions, these equations are readily integrated numerically. The results of these integrations predict the success (into the basket) or failure (off the outside of the rim) of the basketball shot. A series of examples are presented. The examples show that minor changes in the initial conditions can produce major changes in the subsequent ball motion. Shooting and coaching strategies are recommended.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

A basketball rolling on a basket rim

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Figure 2

Overhead view of the ball on the rim

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Figure 3

Horizontal view of the ball on the rim

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Figure 4

Steady-state ball movement around the rim: (a) angles β and γ and (b) angular velocity components

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Figure 5

Ball rolling the rim and falling into the basket: (a) angles β and γ and (b) angular velocity components

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Figure 6

Ball rolling the rim and falling away from the basket: (a) angles β and γ and (b) angular velocity components

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Figure 7

Periodic solution: (a) trajectory and (b) time values for β and β̇

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Figure 8

Ball trajectories for slightly different initial conditions

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