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 Nelin. Dinam., 2017, Volume 13, Number 4, Pages 533–542 (Mi nd583)

On the 75th birthday of A.P.Markeev

Investigation of the dynamics of a two-degrees-of-freedom piecewise linear oscillator

A. E. Baikov, N. V. Kovalev

Moscow Aviation Institute (National Research University), Volokolamskoe sh. 4, Moscow, 125993, Russia

Abstract: The motion of a piecewise linear oscillator is considered. It consists of two spring connected drawers on a conveyor belt moving at a constant speed. The equations of motion are averaged in one nonresonance case. A continuum of invariant tori is obtained that exists in the exact system. The attraction (in finite time) of the trajectories to the family of limit tori is proved (limit tori belong to the continuum of invariant tori). We also investigate zones of sticking, which cannot be detected by averaging.

Keywords: equations with discontinuities, piecewise linear oscillator, averaging method, invariant torus, sticking zone

 Funding Agency Grant Number Russian Science Foundation 14-21-00068

DOI: https://doi.org/10.20537/nd1704006

Full text: PDF file (298 kB)
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UDC: 531.44, 517.928
MSC: 70F40, 70K43, 70K65
Accepted:30.11.2017

Citation: A. E. Baikov, N. V. Kovalev, “Investigation of the dynamics of a two-degrees-of-freedom piecewise linear oscillator”, Nelin. Dinam., 13:4 (2017), 533–542

Citation in format AMSBIB
\Bibitem{BaiKov17} \by A.~E.~Baikov, N.~V.~Kovalev \paper Investigation of the dynamics of a two-degrees-of-freedom piecewise linear oscillator \jour Nelin. Dinam. \yr 2017 \vol 13 \issue 4 \pages 533--542 \mathnet{http://mi.mathnet.ru/nd583} \crossref{https://doi.org/10.20537/nd1704006} \elib{http://elibrary.ru/item.asp?id=30780699}