| Résumé |
Using the approach first pioneered by Raman, the Helmholtz motion of a bowed
string is discussed as a special case of "two-velocity motions," in which a given
point (at which the bow is located ) alternates, in the course of a cycle, between
two constant velocities. The fact that the bow typically presents a negative
resistance to the string during the "slipping" part of the cycle is adduced as a
reason for the "duty cycle," that is, the fraction of the period that corresponds to
slipping, to try to become as short as possible. It is shown that, for a string
without dissipation or stiffness, this duty cycle can be arbitrarily low for general
bow positions; data obtained with the "digital bow" illustrate this behavior. It is
shown theoretically, and confirmed with computer simulations, that instabilities
arising from the negative slipping resistance cannot be eliminated by assigning a
finite positive value to the sticking resistance. The apparent stability of Helmholtz
motion observed in real playing situations remains a puzzle.
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