The Nonlinearly Damped Oscillator
نویسنده
چکیده
We study the large-time behaviour of the nonlinear oscillator mx′′ + f(x′) + k x = 0 , 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′|α−1x′ with α real, A > 0. We characterize the existence and behaviour of fast orbits, i.e, orbits that stop in finite time. Mathematics Subject Classification. 34C15, Nonlinear oscillations.
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