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Rus. J. Nonlin. Dyn., 2020, Volume 16, Number 2, Pages 343–353 (Mi nd714)  

Mathematical problems of nonlinearity

Remarks on Forced Oscillations in Some Systems with Gyroscopic Forces

I. Yu. Polekhin

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: In this paper we study the existence of forced oscillations in two Lagrange systems with gyroscopic forces: a spherical pendulum in a magnetic field and a point on a rotating closed convex surface. We show how it is possible to prove the existence of forced oscillations in these systems provided the systems move in the presence of viscous friction.

Keywords: forced oscillation, spherical pendulum, gyroscopic force, friction, Wazewski method

DOI: https://doi.org/10.20537/nd200208

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MSC: 34C25, 70H12
Received: 09.12.2019
Accepted:26.03.2020
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Citation: I. Yu. Polekhin, “Remarks on Forced Oscillations in Some Systems with Gyroscopic Forces”, Rus. J. Nonlin. Dyn., 16:2 (2020), 343–353

Citation in format AMSBIB
\Bibitem{Pol20}
\by I. Yu. Polekhin
\paper Remarks on Forced Oscillations in Some Systems with Gyroscopic Forces
\jour Rus. J. Nonlin. Dyn.
\yr 2020
\vol 16
\issue 2
\pages 343--353
\mathnet{http://mi.mathnet.ru/nd714}
\crossref{https://doi.org/10.20537/nd200208}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=4126039}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85093897616}


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