The transient behaviour of models of bowed-string motion

Theoretical models of the action of a bowed string may be able to shed light on differences of "playability" between different violins. Subjective judgements seem to be concerned, at least in part, with the robustness with which one particular oscillation regime of the string (the "Helmholtz motion") may be obtained under different bowing conditions. In this paper, after a review of bowed-string modelling, systematic simulation is used to obtain plots of the basin of attraction of the Helmholtz motion in a particular subspace of the player's control space. Variations in the size and structure of this basin of attraction are seen when parameters of the problem are varied, and some physical interpretation of these variations is given. Some parallels and contrasts are pointed out between the particular features of the bowed string as a nonlinear system, and the range of more familiar dynamical systems. (c) 1995 American Institute of Physics.