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Method to Construct Periodic Solutions of Controlled Second-Order Dynamical Systems

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Abstract

Nonconservative mechanical systems with one degree of freedom are considered. The goal is to provide the existence of steady-state oscillations with the prescribed properties. The system’s behavior is modeled by a second-order autonomous dynamical system with one variable parameter describing the amplifying coefficient of the control action. A numerical-analytic method to find the amplifying coefficient is proposed. Conditions of the orbital stability are obtained for the steady-state oscillations. An example of the application of the method is provided. The proposed approach can be applied to solve control problems and to find periodic solutions of second-order autonomous dynamical systems.

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ACKNOWLEDGMENTS

This work was supported by Russian Foundation for Basic Research, project nos. 18-31-20029 and 17-08-01366.

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Authors and Affiliations

  1. Institute of Mechanics, Lomonosov Moscow State University, 119192, Moscow, Russia

    L. A. Klimina & Yu. D. Selyutskiy

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  1. L. A. Klimina
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  2. Yu. D. Selyutskiy
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Correspondence to L. A. Klimina.

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Translated by A. Muravnik

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Klimina, L.A., Selyutskiy, Y.D. Method to Construct Periodic Solutions of Controlled Second-Order Dynamical Systems. J. Comput. Syst. Sci. Int. 58, 503–514 (2019). https://doi.org/10.1134/S1064230719030109

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  • DOI: https://doi.org/10.1134/S1064230719030109

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