Аннотация:
This paper investigates the dynamics of a point vortex and a balanced circular foil
in an ideal fluid. An explicit reduction to quadratures is performed. A bifurcation diagram is
constructed and a classification of the types of integral manifolds is carried out. The stability
of critical solutions is studied in which the foil and the vortex move in a circle or in a straight
line.
The work of I. S. Mamaev (Sections 2 and 5) was carried out within the framework of the state
assignment of the Ministry of Education and Science of Russia (FZZN-2020-0011) and supported
by the RFBR Grant no. 18-29-10050-mk.
The work of I.A. Bizyaev (Sections 3 and 4) was performed at the Ural Mathematical Center
(Agreement no. 075-02-2021-1383).
Поступила в редакцию: 27.09.2021 Принята в печать: 29.10.2021
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Эта публикация цитируется в следующих 5 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
Aleksey Yu. Varaksin, Sergei V. Ryzhkov, “Physical Modeling of Structure and Dynamics of Concentrated, Tornado-like Vortices (A Review)”, Aerospace, 11:10 (2024), 800
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
Leonid Kurakin, Irina Ostrovskaya, “On the influence of circulation on the linear stability of a system of a moving cylinder and two identical parallel vortex filaments”, Bol. Soc. Mat. Mex., 29:3 (2023)
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