Physical Models of Trumpet-like Instruments Detailed Behavior and Model Improvements
Résumé
A simple physical model of trumpet-like instruments is studied. Its functioning is analysed from the point of view of the theory of nonlinear dynamical systems. Using Hopf theorem, it is proved that the system has a unique stable periodic orbit in the vicinity of the principal fixed point. Then the model is improved with a better approximation of a natural instrument sound production. This is done while carefully preserving the possibility of understanding and controlling the behavior of the model.