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

Approximate first integrals of nonlinear oscillators with one-degree of freedom 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ARI - An International Journal for Physical and Engineering Sciences Springer Journals

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

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References (9)

Publisher
Springer Journals
Copyright
Copyright © 1998 by Springer-Verlag
Subject
Earth Sciences; Geotechnical Engineering & Applied Earth Sciences; Geology; Engineering, general
ISSN
1434-5641
eISSN
1434-565X
DOI
10.1007/s007770050062
Publisher site
See Article on Publisher Site

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.

Journal

ARI - An International Journal for Physical and Engineering Sciences – Springer Journals

Published: Apr 24, 2014

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