The dynamical theory of the baseball bat

A theory of the elastic behavior of an irregularly shaped, cylindrically symmetric object is developed and applied to the study of the familiar baseball bat. The normal mode, standing wave patterns of elastic vibrations are obtained and displayed graphically. The lowest 20 normal modes, extending in frequency up to about 3 kHz, are used to study and display the elastic response of the bat in the first few milliseconds after striking a ball. The contribution of the normal mode elastic vibrations to the hit ball speed is also developed, and the consequences for the batter (and fielders) are explored.