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Sbornik: Mathematics, 2016, Volume 207, Issue 12, Pages 1709–1728
DOI: https://doi.org/10.1070/SM8616 (Mi sm8616) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Bifurcations of resonance oscillations and optimization of the trigonometric impulse by the nonsymmetry coefficient

D. V. Kostin

Voronezh State University
English version PDF (566 kB) Citations (4) Russian version article
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DOI: https://doi.org/10.1070/SM8616
Abstract: Methods are given for the approximate calculation of a branch of a resonance oscillation when it bifurcates from a stationary point and for optimizing this branch with respect to the nonsymmetry coefficient, which is defined as the ratio between the largest and the smallest values of the amplitude. It is shown that the optimal values of the base amplitudes are the coefficients of the corresponding Fejér series. The largest value of the nonsymmetry coefficient is calculated exactly.
Bibliography: 18 titles.
Keywords: smooth functional, periodic extremal, bifurcation, nonsymmetry coefficient, Fejér trigonometric series, Lyapunov-Schmidt reduction.
Received: 09.10.2015 and 26.05.2016
Bibliographic databases:
Document Type: Article
UDC: 517.538
MSC: 34A37, 34C23, 34C25
Language: English
Original paper language: Russian
Citation: D. V. Kostin, “Bifurcations of resonance oscillations and optimization of the trigonometric impulse by the nonsymmetry coefficient”, Sb. Math., 207:12 (2016), 1709–1728
Citation in format AMSBIB
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\pages 1709--1728
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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