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JOURNALS // Trudy Matematicheskogo Instituta imeni V.A. Steklova // Archive

Trudy Mat. Inst. Steklova, 2020 Volume 310, Pages 267–279 (Mi tm4112)

This article is cited in 3 papers

Some Results on the Existence of Forced Oscillations in Mechanical Systems

Ivan Yu. Polekhin

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

Abstract: We present sufficient conditions for the existence of forced oscillations in nonautonomous mechanical systems. Previously, similar results have been obtained for systems with friction. The results presented here hold for systems both with and without friction. Some examples are given.

Keywords: forced oscillations, periodic solutions, inverted pendulum, geodesic, Nagumo condition, Lefschetz–Hopf theorem, Ważewski method.

UDC: 517.925.42

Received: December 3, 2019
Revised: December 3, 2019
Accepted: May 26, 2020

DOI: 10.4213/tm4112


 English version:
Proceedings of the Steklov Institute of Mathematics, 2020, 310, 250–261

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