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ЖУРНАЛЫ // Regular and Chaotic Dynamics // Архив

Regul. Chaotic Dyn., 2022, том 27, выпуск 1, страницы 24–42 (Mi rcd1151)

Эта публикация цитируется в 6 статьях

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

Аннотация: 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.

Ключевые слова: ideal fluid, motion in the presence of a source, nonintegrability, scattering map, chaotic scattering.

MSC: 76Bxx,70Exx,37Jxx

Поступила в редакцию: 18.10.2021
Принята в печать: 27.12.2021

Язык публикации: английский

DOI: 10.1134/S1560354722010051



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