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

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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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Authors and Affiliations

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

    V. N. Tkhai

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  1. V. N. Tkhai
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Original Russian Text © V.N. Tkhai, 2011, published in Avtomatika i Telemekhanika, 2011, No. 7, pp. 107–115.

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Tkhai, V.N. Oscillations and stability in quasiautonomous system. II. Critical point of the one-parameter family of periodic motions. Autom Remote Control 72, 1450–1457 (2011). https://doi.org/10.1134/S0005117911070137

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  • DOI: https://doi.org/10.1134/S0005117911070137

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