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.
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.
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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\paper Plate Falling in a Fluid: Regular and Chaotic Dynamics of Finite-dimensional Models
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\pages 345--382
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