Dynamics of basketball-rim interactions |
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| Authors: | H?Okubo Email author" target="_blank">M?HubbardEmail author |
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| Institution: | (1) Department of Mechanical System Engineering, National Defense Academy, Yokosuka, Japan;(2) Department of Mechanical and Aeronautical Engineering, University of California, 95616 Davis, CA, USA |
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| Abstract: | A dynamic model for motion of a basketball on the rim is derived. The model is used to investigate shot success sensitivity
to initial conditions and to search for initial conditions that lead to long rim contact times. Nonlinear ordinary differential
equations describe three components of ball angular velocity and contact point position on the toroidal rim. The model includes
radial ball compliance and dissipation and contains three sub-models describing slipping contact, nonslipping contact and
purely gravitational flight. Switching between the three sub-models depends on contact point velocity and friction forces.
Equivalent radial stiffness and damping constants are estimated using experimental ball force-deflection hysteresis data.
General initial conditions almost always involve slip of the ball on the rim. Bouncing on the rim can also occur. After contact
it is possible for the ball to enter the rim with its centre passing significantly below the rim plane before rising and ultimately
escaping. Exotic quasi-equilibrium periodic circular trajectories exist inside but below the rim plane, relying for their
existence on a combination of centripetal force, friction and gyroscopic precession of radial spin about the contact point.
Trajectories, and consequent ball capture or escape, are extremely sensitive to initial conditions, especially rim contact
position and backspin angular velocity. Backspin aids capture on longrolling trajectories. |
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| Keywords: | basketball dynamics long rolling ball-rim contact |
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