Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 196, Pages 44–49
DOI: https://doi.org/10.36535/0233-6723-2021-196-44-49 (Mi into848) 		 
On the stability of coupled nonlinear oscillators

A. A. Kosov

Matrosov Institute for System Dynamics and Control Theory of Siberian Branch of Russian Academy of Sciences, Irkutsk
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DOI: https://doi.org/10.36535/0233-6723-2021-196-44-49
Abstract: In this paper, we consider the problem of Yu. N. Bibikov on the stability of equilibrium positions of two coupled nonlinear oscillators under the action of conservative perturbing forces. We obtain stability and instability conditions for the case of sufficiently small perturbing forces. Also, we consider the problem of stabilizing an equilibrium position by potential forces when only the relative position of the oscillators is measured and propose the form of a stabilizing potential.
Keywords: nonlinear oscillator, Hamiltonian system with two degrees of freedom, stability, stabilization under incomplete measurement.
Funding agency Grant number
Russian Foundation for Basic Research 19-08-00746
This work was supported by the Russian Foundation for Basic Research (project No. 19-08-00746).
Document Type: Article
UDC: 517.925
MSC: 34D20, 34H15, 70E50
Language: Russian
Citation: A. A. Kosov, “On the stability of coupled nonlinear oscillators”, Differential Equations and Optimal Control, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 196, VINITI, Moscow, 2021, 44–49
Citation in format AMSBIB
\Bibitem{Kos21}
\by A.~A.~Kosov
\paper On the stability of coupled nonlinear oscillators
\inbook Differential Equations and Optimal Control
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 196
\pages 44--49
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into848}
\crossref{https://doi.org/10.36535/0233-6723-2021-196-44-49}
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