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Plate falling in a fluid: Regular and chaotic dynamics of finite-dimensional models

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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).

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Authors and Affiliations

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

    Sergey P. Kuznetsov

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  1. Sergey P. Kuznetsov
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Correspondence to Sergey P. Kuznetsov.

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The article is dedicated to the 65th anniversary of Academician Valery V. Kozlov, with respect and admiration for his contribution to the problem under review

This is a translation of the paper “Motion of a falling card in a fluid: Finite-dimensional models, complex phenomena, and nonlinear dynamics”, Nelin. Din., 2015, vol. 11, no. 1, pp. 3–49, previously published only in Russian.

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Kuznetsov, S.P. Plate falling in a fluid: Regular and chaotic dynamics of finite-dimensional models. Regul. Chaot. Dyn. 20, 345–382 (2015). https://doi.org/10.1134/S1560354715030090

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