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 Regul. Chaotic Dyn., 2015, Volume 20, Issue 3, Pages 345–382 (Mi rcd47)

Plate Falling in a Fluid: Regular and Chaotic Dynamics of Finite-dimensional Models

Sergey P. Kuznetsov

Kotel’nikov’s Institute of Radio Engineering and Electronics of RAS, Saratov Branch, ul. Zelenaya 38, Saratov, 410019 Russia

Abstract: Results are reviewed concerning the planar problem of a plate falling in a resisting medium studied with models based on ordinary differential equations for a small number of dynamical variables. A unified model is introduced to conduct a comparative analysis of the dynamical behaviors of models of Kozlov, Tanabe–Kaneko, Belmonte–Eisenberg–Moses and Andersen–Pesavento–Wang using common dimensionless variables and parameters. It is shown that the overall structure of the parameter spaces for the different models manifests certain similarities caused by the same inherent symmetry and by the universal nature of the phenomena involved in nonlinear dynamics (fixed points, limit cycles, attractors, and bifurcations).

Keywords: body motion in a fluid, oscillations, autorotation, flutter, attractor, bifurcation, chaos, Lyapunov exponent

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation NSH-1726.2014.2 Russian Foundation for Basic Research 14-02-00085 This work was partially supported by a grant of the President of the Russian Federation for leading scientific schools NSH-1726.2014.2 “Fundamental problems of nonlinear dynamics and their applications” and RFBR grant 14-02-00085.

DOI: https://doi.org/10.1134/S1560354715030090

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MSC: 34C15, 76D99, 37E99
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Citation: Sergey P. Kuznetsov, “Plate Falling in a Fluid: Regular and Chaotic Dynamics of Finite-dimensional Models”, Regul. Chaotic Dyn., 20:3 (2015), 345–382

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
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