Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2011, Number 4, Pages 39–45 (Mi vmumm701)  
This article is cited in 2 scientific papers (total in 2 papers)

Mechanics

Self-oscillations of two bodies in the case of nonlinear friction

V. G. Vil'ke, I. L. Shapovalov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (356 kB) Citations (2)
Abstract: The motion of two bodies is studied. One of them is connected to a motionless basis by a spring, whereas the other one is connected with a body moving at a constant speed. The interaction of the bodies is described by a nonlinear friction law with a falling section of the characteristic. The averaged equations of motion are obtained in terms of the canonical action–angle variables. The stationary points corresponding to self-oscillation modes are found and their stability is studied.
Key words: self-oscillating system, nonlinear law of friction.
Funding agency Grant number
Russian Foundation for Basic Research 07-01-00134
08-08-00553
08-01-00600
Received: 22.09.2010
Bibliographic databases:
Document Type: Article
UDC: 531.391
Language: Russian
Citation: V. G. Vil'ke, I. L. Shapovalov, “Self-oscillations of two bodies in the case of nonlinear friction”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2011, no. 4, 39–45
Citation in format AMSBIB
\Bibitem{VilSha11}
\by V.~G.~Vil'ke, I.~L.~Shapovalov
\paper Self-oscillations of two bodies in the case of nonlinear friction
\jour Vestnik Moskov. Univ. Ser.~1. Mat. Mekh.
\yr 2011
\issue 4
\pages 39--45
\mathnet{http://mi.mathnet.ru/vmumm701}
\zmath{https://zbmath.org/?q=an:06774422}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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