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Avtomat. i Telemekh., 2011, Issue 7, Pages 107–115 (Mi at2249)  

This article is cited in 4 scientific papers (total in 4 papers)

Nonlinear Systems

Oscillations and stability in quasiautonomous system. II. Critical point of the one-parameter family of periodic motions

V. N. Tkhai

Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

Abstract: Consideration was given to the single-frequency oscillations of a periodic system allied to the nonlinear autonomous system. The publications of the present author demonstrated that the period on the family of oscillations of the autonomous system usually depends only on a single parameter. At that, the points of the family are divided into the ordinary (the derivative with respect to the period in parameter is other than zero) and critical (this derivative vanishes) points. Origination of oscillations at the critical point was studied. It was established that at least two resonance oscillations are generated. The first part of the paper considered the ordinary point.

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English version:
Automation and Remote Control, 2011, 72:7, 1450–1457

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Presented by the member of Editorial Board: Л. Б. Рапопорт

Received: 17.02.2011

Citation: V. N. Tkhai, “Oscillations and stability in quasiautonomous system. II. Critical point of the one-parameter family of periodic motions”, Avtomat. i Telemekh., 2011, no. 7, 107–115; Autom. Remote Control, 72:7 (2011), 1450–1457

Citation in format AMSBIB
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\by V.~N.~Tkhai
\paper Oscillations and stability in quasiautonomous system.~II. Critical point of the one-parameter family of periodic motions
\jour Avtomat. i Telemekh.
\yr 2011
\issue 7
\pages 107--115
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\zmath{https://zbmath.org/?q=an:05979856}
\transl
\jour Autom. Remote Control
\yr 2011
\vol 72
\issue 7
\pages 1450--1457
\crossref{https://doi.org/10.1134/S0005117911070137}
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    Citing articles on Google Scholar: Russian citations, English citations
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    Cycle of papers

    This publication is cited in the following articles:
    1. V. N. Tkhai, “Model with coupled subsystems”, Autom. Remote Control, 74:6 (2013), 919–931  mathnet  crossref  mathscinet  isi
    2. I. N. Barabanov, V. N. Tkhai, “Quasi-Autonomous Systems: Oscillations, Stability, and Stabilization in the Regular Point of the Family of Periodic Solutions”, Autom. Remote Control, 74:8 (2013), 1257–1268  mathnet  crossref  isi  elib  elib
    3. Tkhai V.N., “A Mechanical System Containing Weakly Coupled Subsystems”, Pmm-J. Appl. Math. Mech., 77:6 (2013), 588–594  crossref  isi  scopus
    4. I. N. Barabanov, A. T. Tureshbaev, V. N. Tkhai, “Basic oscillation mode in the coupled-subsystems model”, Autom. Remote Control, 75:12 (2014), 2112–2123  mathnet  crossref  isi
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