Dynamical systems and physical models of trumpet-like instruments. Analytical study and asymptotical properties

摘要

A simple physical model of trumpet-like instruments for real-time synthesis is described. Its functioning is analysed from the viewpoint of the theory of nonlinear dynamical systems. Using the Hopf theorem, it is proved that the system has a unique stable periodic orbit in the vicinity of the equilibrium point. An estimate of amplitude and frequency of this periodic orbit is calculated. Different improvements are then brought to the basic model. We study the consequence of each improvement on the ability of both understanding and controling the model's behavior. [References: 49]