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Regular and Chaotic Dynamics, 2022, Volume 27, Issue 1, Pages 24–42
DOI: https://doi.org/10.1134/S1560354722010051
(Mi rcd1151)
 

This article is cited in 6 scientific papers (total in 6 papers)

The Motion of an Unbalanced Circular Disk in the Field of a Point Source

Elizaveta M. Artemovaa, Evgeny V. Vetchaninb

a Ural Mathematical Center, Udmurt State University, ul. Universitetskaya 1, 426034 Izhevsk, Russia
b Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, 426069 Izhevsk, Russia
Citations (6)
References:
Abstract: Describing the phenomena of the surrounding world is an interesting task that has long attracted the attention of scientists. However, even in seemingly simple phenomena, complex dynamics can be revealed. In particular, leaves on the surface of various bodies of water exhibit complex behavior. This paper addresses an idealized description of the mentioned phenomenon. Namely, the problem of the plane-parallel motion of an unbalanced circular disk moving in a stream of simple structure created by a point source (sink) is considered. Note that using point sources, it is possible to approximately simulate the work of skimmers used for cleaning swimming pools. Equations of coupled motion of the unbalanced circular disk and the point source are derived. It is shown that in the case of a fixed-position source of constant intensity the equations of motion of the disk are Hamiltonian. In addition, in the case of a balanced circular disk the equations of motion are integrable. A bifurcation analysis of the integrable case is carried out. Using a scattering map, it is shown that the equations of motion of the unbalanced disk are nonintegrable. The nonintegrability found here can explain the complex motion of leaves in surface streams of bodies of water.
Keywords: ideal fluid, motion in the presence of a source, nonintegrability, scattering map, chaotic scattering.
Funding agency Grant number
Ministry of Education and Science of the Russian Federation FEWS-2020-0009
Russian Foundation for Basic Research 18-29-10050-mk
The work of Elizaveta M. Artemova (Sections 2 and 4) was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (FEWS-2020-0009), and was supported in part by the Moebius Contest Foundation for Young Scientists. The work of Evgeny V. Vetchanin (Sections 1 and 3) is supported by the RFBR under grant 18-29-10050-mk.
Received: 18.10.2021
Accepted: 27.12.2021
Bibliographic databases:
Document Type: Article
Language: English
Citation: Elizaveta M. Artemova, Evgeny V. Vetchanin, “The Motion of an Unbalanced Circular Disk in the Field of a Point Source”, Regul. Chaotic Dyn., 27:1 (2022), 24–42
Citation in format AMSBIB
\Bibitem{ArtVet22}
\by Elizaveta M. Artemova, Evgeny V. Vetchanin
\paper The Motion of an Unbalanced Circular Disk
in the Field of a Point Source
\jour Regul. Chaotic Dyn.
\yr 2022
\vol 27
\issue 1
\pages 24--42
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\crossref{https://doi.org/10.1134/S1560354722010051}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85124401099}
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  • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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