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Motion of a Smooth Foil in a Fluid under the Action of External Periodic Forces. I

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Abstract

A plane-parallel motion of a circular foil is considered in a fluid with a nonzero constant circulation under the action of external periodic force and torque. Various integrable cases are treated. Conditions for the existence of resonances of two types are found. In the case of resonances of the first type, the phase trajectory of the system and the trajectory of the foil are unbounded. In the case of resonances of the second type, the foil trajectory is unbounded, while the phase trajectory of the system remains bounded during the motion.

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Acknowledgment

The authors are grateful to I. A. Bizyaev, S. P. Kuznetsov, and D. V. Treschev for valuable comments and productive discussions.

Funding

The work of A. V. Borisov was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (1.2404.2017/4.6). The work of E. V. Vetchanin 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 18-08-00995-a. 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. I. Russ. J. Math. Phys. 26, 412–427 (2019). https://doi.org/10.1134/S1061920819040022

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