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.
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.
Поступила в редакцию: 18.10.2021 Принята в печать: 27.12.2021
Образец цитирования:
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
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\paper The Motion of an Unbalanced Circular Disk
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\jour Regul. Chaotic Dyn.
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Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1151
https://www.mathnet.ru/rus/rcd/v27/i1/p24
Эта публикация цитируется в следующих 6 статьяx:
Elizaveta Artemova, Evgeny Vetchanin, “The motion of a circular foil in the field of a fixed point singularity: Integrability and asymptotic behavior”, Physics of Fluids, 36:2 (2024)
Evgeny V. Vetchanin, Ivan S. Mamaev, “Numerical Analysis of a Drop-Shaped Aquatic Robot”, Mathematics, 12:2 (2024), 312
Stephan Eckstein, Gudmund Pammer, “Computational methods for adapted optimal transport”, Ann. Appl. Probab., 34:1A (2024)
Mathias Beiglböck, Benjamin Jourdain, William Margheriti, Gudmund Pammer, “Stability of the weak martingale optimal transport problem”, Ann. Appl. Probab., 33:6B (2023)
Ivan A. Bizyaev, Ivan S. Mamaev, “Dynamics of a Circular Foil and Two Pairs of Point Vortices: New Relative Equilibria and a Generalization of Helmholtz Leapfrogging”, Symmetry, 15:3 (2023), 698
Е. В. Ветчанин, И. С. Мамаев, “Периодическое возмущение движения неуравновешенного кругового профиля в присутствии точечных вихрей в идеальной жидкости”, Вестн. Удмуртск. ун-та. Матем. Мех. Компьют. науки, 32:4 (2022), 630–643
Цитирование в формате AMSBIB
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