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Approximate First Integrals of Weakly Nonlinear, Damped-Driven Oscillators with One Degree of Freedom

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Abstract

First-order approximate symmetries of weaklynonlinear, damped-driven oscillators have been determined.First-order approximate first integrals have been obtained byemploying an approximate version of Noether's theorem for the conservativecase. Furthermore, approximate first integrals of the damped case have been obtained based on the first integrals of the conservative case.Approximate first integrals enabled us to identify three types of genericbifurcations. Analytical results have been verified by numerical experiments.

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Authors and Affiliations

  1. Faculty of Science and Letters, Istanbul Technical University, Maslak 80626, Istanbul, Turkey

    Gazanfer Unal

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  1. Gazanfer Unal
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Unal, G. Approximate First Integrals of Weakly Nonlinear, Damped-Driven Oscillators with One Degree of Freedom. Nonlinear Dynamics 26, 309–329 (2001). https://doi.org/10.1023/A:1013331523696

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  • DOI: https://doi.org/10.1023/A:1013331523696

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