2006 International Conference in honor of Jacqueline Fleckinger. Electron. J. Diff. Eqns., Conference 16 (2007), pp. 95-102.

Asymptotic behavior of a weakly forced dry friction oscillator

J. Ildefonso Diaz, Georg Hetzer

This note is devoted to stick-slip aspects of the motion of a dry friction damped oscillator under weak irregular forcing. Our main result complements [10, Theorem 3.(a)] and is also related to [1], where a non-Lipschitz model for Coulomb friction was consider in the unforced case. We provide sufficient conditions guaranteeing that solutions stabilizing in finite time, but observe also an infinite succession of ``stick-slip'' behavior. The last section discusses an extension to certain systems of such oscillators.

Published May 15, 2007.
Math Subject Classifications: 34A60, 34D05.
Key Words: Nonlinear oscillators and systems; dry friction; dead zone; extinction in finite time; stick-slip motion.

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Jesus Ildefonso Díaz
Departamento de Matemática Aplicada
Universidad Complutense de Madrid, 28040 Madrid, Spain
email: ji_diaz@mat.ucm.es
Georg Hetzer
Department of Mathematics and Statistics
Auburn University, AL 36849-5310, USA
email: hetzege@auburn.edu

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