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

G. Ünal; A. Kiriş

doi:10.1007/s007770050062

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

G. Ünal^*
, A. Kiriş

^*Bu çalışma için yazışmadan sorumlu yazar

Matematik Bölümü

Istanbul Technical University

Araştırma sonucu: Dergiye katkı › Makale › bilirkişi

Özet

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.

Orijinal dil	İngilizce
Sayfa (başlangıç-bitiş)	258-267
Sayfa sayısı	10
Dergi	Bulletin of the Technical University of Istanbul
Hacim	51
Basın numarası	4
DOI'lar	https://doi.org/10.1007/s007770050062
Yayın durumu	Yayınlandı - 1999

Belgeye Erişim

10.1007/s007770050062

Diğer Dosyalar ve Linkler

Link to publication in Scopus

Alıntı Yap

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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.",

keywords = "Approximate first integrals, Approximate symmetries, Oscillators, Resonances, Symmetry-breaking",

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language = "English",

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T1 - Approximate first integrals of nonlinear oscillators with one-degree of freedom

AU - Ünal, G.

AU - Kiriş, A.

PY - 1999

Y1 - 1999

N2 - 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.

AB - 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.

KW - Approximate first integrals

KW - Approximate symmetries

KW - Oscillators

KW - Resonances

KW - Symmetry-breaking

UR - https://www.scopus.com/pages/publications/27644547192

U2 - 10.1007/s007770050062

DO - 10.1007/s007770050062

M3 - Article

AN - SCOPUS:27644547192

SN - 0254-4121

VL - 51

SP - 258

EP - 267

JO - Bulletin of the Technical University of Istanbul

JF - Bulletin of the Technical University of Istanbul

IS - 4

ER -

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

Özet

Belgeye Erişim

Diğer Dosyalar ve Linkler

Parmak izi

Alıntı Yap