An Application of the Melnikov Method to a Piecewise Oscillator
| Autor: | Oltiana Gjata, Fabio Zanolin |
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| Rok vydání: | 2023 |
| Předmět: | |
| Zdroj: | Contemporary Mathematics. :249-269 |
| ISSN: | 2705-1056 2705-1064 |
| DOI: | 10.37256/cm.4220232160 |
| Popis: | In this paper we present a new application of the Melnikov method to a class of periodically perturbed Duffing equations where the nonlinearity is non-smooth as otherwise required in the classical applications. Extensions of the Melnikov method to these situations is a topic with growing interests from the researchers in the past decade. Our model, motivated by the study of mechanical vibrations for systems with ''stops'', considers a case of a nonlinear equation with piecewise linear components. This allows us to provide a precise analytical representation of the homoclinic orbit for the associated autonomous planar system and thus obtain simply computable conditions for the zeros of the associated Melnikov function. |
| Databáze: | OpenAIRE |
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