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Section
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Mechanics
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Title
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Periodic perturbation of motion of an unbalanced circular foil in the presence of point vortices in an ideal fluid
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Author(-s)
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Vetchanin E.V.a,
Mamaev I.S.a
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Affiliations
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Udmurt State Universitya
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Abstract
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The dynamics of a system governing the controlled motion of an unbalanced circular foil in the presence of point vortices is considered. The foil motion is controlled by periodically changing the position of the center of mass, the gyrostatic momentum, and the moment of inertia of the system. A derivation of the equations of motion based on Sedov's approach is proposed, the equations of motion are presented in the Hamiltonian form. A periodic perturbation of the known integrable case is considered.
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Keywords
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motion in an ideal fluid, point vortices, period perturbation, vortex-body interaction
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UDC
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532.3, 517.933
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MSC
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70E60, 37N35
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DOI
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10.35634/vm220409
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Received
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15 October 2022
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Language
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Russian
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Citation
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Vetchanin E.V., Mamaev I.S. Periodic perturbation of motion of an unbalanced circular foil in the presence of point vortices in an ideal fluid, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2022, vol. 32, issue 4, pp. 630-643.
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References
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- Borisov A.V., Mamaev I.S. Matematicheskie metody v dinamike vikhrevykh struktur (Mathematical methods in the dynamics of vortex structures), Moscow-Izhevsk: Institute of Computer Science, 2005.
- Kochin N.E., Kibel I.A., Roze N.V. Theoretical hydrodynamics, New York: Wiley, 1964.
- Sedov L.I. Ploskie zadachi gidrodinamiki i aerodinamiki (Two-dimensional problems in hydro- and aeromechanics), Moscow-Leningrad: GITTL, 1950.
- Vetchanin E.V., Kilin A.A. Free and controlled motion of a body with moving internal mass through a fluid in the presence of circulation around the body, Doklady Physics, 2016, vol. 61, issue 1, pp. 32-36. http://doi.org/10.1134/S1028335816010110
- Artemova E.M., Vetchanin E.V. The motion of an unbalanced circular disk in the field of a point source, Regular and Chaotic Dynamics, 2022, vol. 27, issue 1, pp. 24-42. http://doi.org/10.1134/S1560354722010051
- Borisov A.V., Mamaev I.S. On the motion of a heavy rigid body in an ideal fluid with circulation, Chaos: An Interdisciplinary Journal of Nonlinear Science, 2006, vol. 16, no. 1, 013118. http://doi.org/10.1063/1.2166530
- Borisov A.V., Mamaev I.S., Vetchanin E.V. Self-propulsion of a smooth body in a viscous fluid under periodic oscillations of a rotor and circulation, Regular and Chaotic Dynamics, 2018, vol. 23, issues 7-8, pp. 850-874. http://doi.org/10.1134/S1560354718070043
- Borisov A.V., Mamaev I.S., Ramodanov S.M. Motion of a circular cylinder and $n$ point vortices in a perfect fluid, Regular and Chaotic Dynamics, 2003, vol. 8, issue 4, pp. 449-462. http://doi.org/10.1070/RD2003v008n04ABEH000257
- Llewellyn Smith S.G. How do singularities move in potential flow?, Physica D: Nonlinear Phenomena, 2011, vol. 240, issue 20, pp. 1644-1651. https://doi.org/10.1016/j.physd.2011.06.010
- Mamaev I.S., Bizyaev I.A. Dynamics of an unbalanced circular foil and point vortices in an ideal fluid, Physics of Fluids, 2021, vol. 33, issue 8, 087119. http://doi.org/10.1063/5.0058536
- Mason R.J. Fluid Locomotion and Trajectory Planning for Shape-Changing Robots, PhD Dissertation, Pasadena, Calif.: California Institute of Technology, 2003, 264 pp.
- Michelin S., Llewellyn Smith S.G. An unsteady point vortex method for coupled fluid-solid problems, Theoretical and Computational Fluid Dynamics, 2009, vol. 23, issue 2, pp. 127-153. https://doi.org/10.1007/s00162-009-0096-7
- Ramodanov S.M. Motion of a circular cylinder and a vortex in an ideal fluid, Regular and Chaotic Dynamics, 2001, vol. 6, no. 1, pp. 33-38. https://doi.org/10.1070/RD2001v006n01ABEH000163
- Ramodanov S.M. Motion of a circular cylinder and $N$ point vortices in a perfect fluid, Regular and Chaotic Dynamics, 2002, vol. 7, no. 3, pp. 291-298. https://doi.org/10.1070/RD2002v007n03ABEH000211
- Shashikanth B.N., Marsden J.E., Burdick J.W., Kelly S.D. The Hamiltonian structure of a 2D rigid circular cylinder interacting dynamically with $N$ point vortices, Physics of Fluids, 2002, vol. 14, issue 3, pp. 1214-1227. https://doi.org/10.1063/1.1445183
- Vetchanin E.V., Kilin A.A. Control of body motion in an ideal fluid using the internal mass and the rotor in the presence of circulation around the body, Journal of Dynamical and Control Systems, 2017, vol. 23, issue 2, pp. 435-458. https://doi.org/10.1007/s10883-016-9345-4
- Vetchanin E.V., Mikishanina E.A. Vibrational stability of periodic solutions of the Liouville equations, Russian Journal of Nonlinear Dynamics, 2019, vol. 15, no. 3, pp. 351-363. https://doi.org/10.20537/nd190312
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