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.
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
\Bibitem{Kos16}
\by D.~V.~Kostin
\paper Bifurcations of resonance oscillations and optimization of the trigonometric impulse by the nonsymmetry coefficient
\jour Sb. Math.
\yr 2016
\vol 207
\issue 12
\pages 1709--1728
\mathnet{http://mi.mathnet.ru/eng/sm8616}
\crossref{https://doi.org/10.1070/SM8616}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3588987}
\zmath{https://zbmath.org/?q=an:1364.34051}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2016SbMat.207.1709K}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000394542200005}
\elib{https://elibrary.ru/item.asp?id=27485044}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014201194}
Linking options:
https://www.mathnet.ru/eng/sm8616
https://doi.org/10.1070/SM8616
https://www.mathnet.ru/eng/sm/v207/i12/p90
This publication is cited in the following 4 articles:
A. V. Zhurba, S. D. Baboshin, T. I. Kostina, P. Reino de Fitt, “O matematicheskoi modeli protsessa impulsnogo vibropogruzheniya i ego ustoichivosti”, Chelyab. fiz.-matem. zhurn., 7:2 (2022), 152–163
D. V. Kostin, T. I. Kostina, A. V. Zhurba, A. S. Myznikov, “Nelineinaya matematicheskaya model impulsnogo pogruzhatelya”, Chelyab. fiz.-matem. zhurn., 6:1 (2021), 34–41
T I Kostina, M N Silaeva, Alkadi Hamsa Mohamad, M U Pritsepov, “Solution of the Mainardi Signaling Problems with the Maxwell-Fejer impulse”, J. Phys.: Conf. Ser., 1902:1 (2021), 012038
Dmitriy V Kostin, Tatiana I Kostina, Leonid V Stenyuhin, “On the existence of extremals of some nonlinear Fredholm operators”, J. Phys.: Conf. Ser., 1203 (2019), 012066
Citation in format AMSBIB
Contact us: