Dynamics of the Interactions between Ball, Strings, and Racket in Tennis

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Abstract
The dynamical interactions in tennis between ball, strings, and racket, during ball impact and immediately after, are modeled by a system of nonlinear ordinary differential equations that include both damping and elastic properties. During impact, the time history of the deflections, velocities, and forces in all parts of the system were calculated. Some simple experiments were done to determine the elastic and damping properties of the ball and strings, and to verify the theory in the case of a ball rebounding from the strings of a clamped racket head. Among the findings is that there is a trampoline effect even for a clamped racket head. Most interesting is that the rebound velocity of the ball can be increased, the mechanical energy transmitted to the racket can be reduced, and the maximum force transmitted to the holder of the racket can be reduced, all by increasing the damping in the racket.

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