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

This article is cited in 21 scientific papers (total in 21 papers)

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.


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MSC: 34C15, 76D99, 37E99
Received: 22.11.2014

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

Citation in format AMSBIB
\by Sergey P. Kuznetsov
\paper Plate Falling in a Fluid: Regular and Chaotic Dynamics of Finite-dimensional Models
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 345--382

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    This publication is cited in the following articles:
    1. S. V. Sokolov, “On the problem of falling motion of a circular cylinder and a vortex pair in a perfect fluid”, Dokl. Math., 94:2 (2016), 594–597  crossref  crossref  mathscinet  zmath  isi  elib  scopus
    2. Sergey P. Kuznetsov, “Hyperbolic Chaos in Self-oscillating Systems Based on Mechanical Triple Linkage: Testing Absence of Tangencies of Stable and Unstable Manifolds for Phase Trajectories”, Regul. Chaotic Dyn., 20:6 (2015), 649–666  mathnet  crossref  mathscinet  adsnasa
    3. Sergey P. Kuznetsov, Vyacheslav P. Kruglov, “Verification of Hyperbolicity for Attractors of Some Mechanical Systems with Chaotic Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 160–174  mathnet  crossref  mathscinet
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    5. S. P. Kuznetsov, “Parametric chaos generator operating on a varactor diode with the instability limitation decay mechanism”, Tech. Phys., 61:3 (2016), 436–445  crossref  isi  scopus
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    7. Ivan A. Bizyaev, Alexey V. Borisov, Ivan S. Mamaev, “The Chaplygin Sleigh with Parametric Excitation: Chaotic Dynamics and Nonholonomic Acceleration”, Regul. Chaotic Dyn., 22:8 (2017), 955–975  mathnet  crossref
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    9. E. M. Lau, W.-X. Huang, Ch.-X. Xu, “Progression of heavy plates from stable falling to tumbling flight”, J. Fluid Mech., 850 (2018), 1009–1031  crossref  zmath  isi  scopus
    10. A. B. Rostami, A. C. Fernandes, “Mathematical model and stability analysis of fluttering and autorotation of an articulated plate into a flow”, Commun. Nonlinear Sci. Numer. Simul., 56 (2018), 544–560  crossref  mathscinet  isi  scopus
    11. E. V. Vetchanin, E. S. Gladkov, “Identifikatsiya parametrov modeli dvizheniya toroidalnogo tela na osnove eksperimentalnykh dannykh”, Nelineinaya dinam., 14:1 (2018), 99–121  mathnet  crossref  elib
    12. Alexey V. Borisov, Ivan S. Mamaev, Eugeny V. Vetchanin, “Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation”, Regul. Chaotic Dyn., 23:4 (2018), 480–502  mathnet  crossref  mathscinet
    13. Alexey V. Borisov, Sergey P. Kuznetsov, “Comparing Dynamics Initiated by an Attached Oscillating Particle for the Nonholonomic Model of a Chaplygin Sleigh and for a Model with Strong Transverse and Weak Longitudinal Viscous Friction Applied at a Fixed Point on the Body”, Regul. Chaotic Dyn., 23:7-8 (2018), 803–820  mathnet  crossref
    14. Alexey V. Borisov, Ivan S. Mamaev, Evgeny V. Vetchanin, “Self-propulsion of a Smooth Body in a Viscous Fluid Under Periodic Oscillations of a Rotor and Circulation”, Regul. Chaotic Dyn., 23:7-8 (2018), 850–874  mathnet  crossref
    15. I. S. Mamaev, V. A. Tenenev, E. V. Vetchanin, “Dynamics of a Body with a Sharp Edge in a Viscous Fluid”, Nelin. Dinam., 14:4 (2018), 473–494  mathnet  crossref  elib
    16. T. Lam, L. Vincent, E. Kanso, “Passive flight in density-stratified fluids”, J. Fluid Mech., 860 (2018), 200–223  crossref  mathscinet  isi
    17. A. B. Rostami, A. C. Fernandes, “Evaluation of dynamics of fluttering and autorotation of a rigid plate in a flow using far-field method”, Nonlinear Dyn., 94:3 (2018), 1619–1638  crossref  mathscinet  isi  scopus
    18. E. V. Vetchanin, “The Motion of a Balanced Circular Cylinder in an Ideal Fluid Under the Action of External Periodic Force and Torque”, Rus. J. Nonlin. Dyn., 15:1 (2019), 41–57  mathnet  crossref  elib
    19. V A. Borisov , E. V. Vetchanin, I. S. Mamaev, “Motion of a smooth foil in a fluid under the action of external periodic forces. I”, Russ. J. Math. Phys., 26:4 (2019), 412–427  crossref  mathscinet  zmath  isi  scopus
    20. T. Howison, J. Hughes, F. Giardina, F. Iida, “Physics driven behavioural clustering of free-falling paper shapes”, PLoS One, 14:6 (2019), e0217997  crossref  isi  scopus
    21. T. A. Gurina, “Bifurkatsionnoe issledovanie perekhoda k khaosu v kolebatelnoi sisteme dvizheniya plastinki v zhidkosti”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 29:1 (2019), 3–18  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
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