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Abstract
We introduce a new analytical method, which allows to find chaotic regimes in non-smooth dynamical systems. A simple mechanical system consisting of a mass and a dry friction element is considered. The corresponding mathematical model is being studied. We show that the considered dynamical system is a skew product over a piecewise smooth mapping of a segment (the so-called base map). For this base map we demonstrate existence of a domain of parameters where a chaotic dynamics can be observed. We prove existence of an infinite set of periodic points of arbitrarily big period. Moreover, a reduction of the considered map to a compact subset of the segment is semi-conjugated to a shift on the set of one-sided infinite boolean sequences. We find conditions, sufficient for existence of a superstable periodic point of the base map. The obtained result partially solves a general problem: theoretical confirmation of chaotic and periodic regimes numerically and experimentally observed for models of percussion drilling.
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Authors (2)
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Nikita Begun PhD
- Saint Petersburg State University, Russia
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Cite as
Full text
- Publication version
- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s11012-014-0071-2
- License
- Copyright (2015 Springer Science+Business Media Dordrecht)
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Details
- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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MECCANICA
no. 50,
pages 1935 - 1948,
ISSN: 0025-6455 - Language:
- English
- Publication year:
- 2015
- Bibliographic description:
- Begun N., Kryzhevich S.: 0025-6455// MECCANICA -, (2015), s.1935-1948
- DOI:
- Digital Object Identifier (open in new tab) 10.1007/s11012-014-0071-2
- Sources of funding:
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- Free publication
- Verified by:
- Gdańsk University of Technology
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