Abstract
This paper considers the plane-parallel motion of an elliptic foil in a fluid with a nonzero constant circulation under the action of external periodic forces and torque. The existence of the first integral is shown for the case in which there is no external torque and an external force acts along one of the principal axes of the foil. It is shown that, in the general case, in the absence of friction, an extensive stochastic layer is observed for the period advance map. When dissipation is added to the system, strange attractors can arise from the stochastic layer.
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Acknowledgment
The authors express their gratitude to I. A. Bizyaev, S. P. Kuznetsov, and D. V. Treshchev for valuable remarks and fruitful discussions.
Funding
The work of E. V. Vetchanin (Sections 2, 3) was supported by the Russian Science Foundation under grant 18-71-00111.
The work of I. S. Mamaev was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (1.2405.2017/4.6) and is supported by the RFBR under grant 18-29-10050-mk.
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Borisov, A.V., Vetchanin, E.V. & Mamaev, I.S. Motion of a Smooth Foil in a Fluid under the Action of External Periodic Forces. II. Russ. J. Math. Phys. 27, 1–17 (2020). https://doi.org/10.1134/S106192082001001X
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DOI: https://doi.org/10.1134/S106192082001001X