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One-dimensional chaos in a system with dry friction: analytical approach. / Begun, N.; Kryzhevich, S.

In: Meccanica, Vol. 50, No. 8, 2015, p. 1935-1948.

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Begun, N. ; Kryzhevich, S. / One-dimensional chaos in a system with dry friction: analytical approach. In: Meccanica. 2015 ; Vol. 50, No. 8. pp. 1935-1948.

BibTeX

@article{bc5766e0624542d28f800e61baa9c916,
title = "One-dimensional chaos in a system with dry friction: analytical approach",
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.",
keywords = "Chaos 􏱮 Mappings of segments 􏱮 Dry friction 􏱮 Filippov systems 􏱮 Turbulence",
author = "N. Begun and S. Kryzhevich",
year = "2015",
doi = "10.1007/s11012-014-0071-2",
language = "English",
volume = "50",
pages = "1935--1948",
journal = "Meccanica",
issn = "0025-6455",
publisher = "Springer Nature",
number = "8",

}

RIS

TY - JOUR

T1 - One-dimensional chaos in a system with dry friction: analytical approach

AU - Begun, N.

AU - Kryzhevich, S.

PY - 2015

Y1 - 2015

N2 - 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.

AB - 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.

KW - Chaos 􏱮 Mappings of segments 􏱮 Dry friction 􏱮 Filippov systems 􏱮 Turbulence

U2 - 10.1007/s11012-014-0071-2

DO - 10.1007/s11012-014-0071-2

M3 - Article

VL - 50

SP - 1935

EP - 1948

JO - Meccanica

JF - Meccanica

SN - 0025-6455

IS - 8

ER -

ID: 3976867