We prove the existence of a periodic solution to a nonlinear impact oscillator, whose restoring force has an asymptotically linear behavior. To this aim, after regularizing the problem, we use phase-plane analysis, and apply the Poincaré-Bohl fixed point Theorem to the associated Poincaré map, so to find a periodic solution of the regularized problem. Passing to the limit, we eventually find the "bouncing solution'' we are looking for.
Periodic bouncing solutions for nonlinear impact oscillators
FONDA, ALESSANDRO;SFECCI, ANDREA
2013-01-01
Abstract
We prove the existence of a periodic solution to a nonlinear impact oscillator, whose restoring force has an asymptotically linear behavior. To this aim, after regularizing the problem, we use phase-plane analysis, and apply the Poincaré-Bohl fixed point Theorem to the associated Poincaré map, so to find a periodic solution of the regularized problem. Passing to the limit, we eventually find the "bouncing solution'' we are looking for.File in questo prodotto:
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