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Approximate first integrals of nonlinear oscillators with one-degree of freedom

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ARI - An International Journal for Physical and Engineering Sciences

Abstract

Exact symmetries of the unperturbed (linear) part of the dynamical systems are determined. Resonance conditions which lead to the symmetry-breaking of the symmetries of the unperturbed part are obtained. The second-order approximate symmetries of the one degree of freedom, damped-driven oscillators are found. By employing an approximate version of Noether’s theorem, second-order approximate first integrals are obtained for undamped oscillators. The results are discussed on the contour plots of the first integrals.

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Authors and Affiliations

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

    G. Ünal & A. Kırış

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  1. G. Ünal
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  2. A. Kırış
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Correspondence to G. Ünal.

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Ünal, G., Kırış, A. Approximate first integrals of nonlinear oscillators with one-degree of freedom. ARI 51, 258–267 (1998). https://doi.org/10.1007/s007770050062

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  • DOI: https://doi.org/10.1007/s007770050062

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