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Regular and Chaotic Dynamics

, Volume 20, Issue 3, pp 345–382 | Cite as

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

  • Sergey P. Kuznetsov
Article

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 

MSC2010 numbers

34C15 76D99 37E99 

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Saratov BranchKotel’nikov’s Institute of Radio Engineering and Electronics of RASSaratovRussia

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