The nonlinearly damped oscillator

Abstract

We study the large-time behaviour of the nonlinear oscillator (Formula Presented), where m; k > 0 and f is a monotone real function representing nonlinear friction. We are interested in understanding the long-time effect of a nonlinear damping term, with special attention to the model case f(x’) = A|x’|± − 1 x’ with ± real, A > 0. We characterize the existence and behaviour of fast orbits, i.e., orbits that stop in innite time. © 2003 EDP Sciences, SMAI.