Physical modeling and sound synthesis of the hi-hat

In this paper, we propose a physical model of the hi-hat. Two cymbals are modeled with thin spherical shells, into which a point mass resembling a stick collides. Two models are proposed for the collision of two cymbals: a spring model and an algorithmically mimicked inelastic collision model. The governing equations for the two proposed models are derived, discretized using the finite difference method, and analyzed numerically. Several numerical experiments have revealed the validity of the two proposed models and the characteristics of the hi-hat.