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Asymptotic behavior in the dynamics of a smooth body in an ideal fluid

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Abstract

This paper addresses a conservative system describing the motion of a smooth body in an ideal fluid under the action of an external periodic torque with nonzero mean and of an external periodic force. It is shown that, in the case where the body is circular in shape, the angular velocity of the body increases indefinitely (linearly in time), and the projection of the phase trajectory onto the plane of translational velocities is attracted to a circle. Asymptotic orbital stability (or asymptotic stability with respect to part of variables) exists in the system. It is shown numerically that, in the case of an elliptic body, the projection of the phase trajectory onto the plane of translational velocities is attracted to an annular region.

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Acknowledgements

The authors extend their gratitude to A. V. Borisov for valuable comments.

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Authors and Affiliations

  1. Udmurt State University, ul. Universitetskaya 1, Izhevsk, Russia, 426034

    Evgeny V. Vetchanin

  2. Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, Russia, 426069

    Evgeny V. Vetchanin & Ivan S. Mamaev

Authors
  1. Evgeny V. Vetchanin
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  2. Ivan S. Mamaev
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Correspondence to Evgeny V. Vetchanin.

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The work of E.V. Vetchanin and I.S. Mamaev was carried out within the framework of the state assignment of the Ministry of Science and Higher Education of Russia (Projects FEWS-2020-0009 and FZZN-2020-0011, respectively). Also this work is supported by the RFBR under Grants 18-08-00995-a and 18-29-10050-mk.

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Vetchanin, E.V., Mamaev, I.S. Asymptotic behavior in the dynamics of a smooth body in an ideal fluid. Acta Mech 231, 4529–4535 (2020). https://doi.org/10.1007/s00707-020-02791-8

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  • DOI: https://doi.org/10.1007/s00707-020-02791-8

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