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Nelin. Dinam., 2016, Volume 12, Number 1, Pages 99–120 (Mi nd515)  

This article is cited in 6 scientific papers (total in 6 papers)

Original papers

Chaotic dynamics in the problem of the fall of a screw-shaped body in a fluid

V. A. Teneneva, E. V. Vetchaninba, L. Ilaletdinova

a Izhevsk State Technical University, Studencheskaya 7, Izhevsk, 426069 Russia
b Udmurt State University, Universitetskaya 1, Izhevsk, 426034 Russia

Abstract: This paper is concerned with the process of the free fall of a three-bladed screw in a fluid. The investigation is performed within the framework of theories of an ideal fluid and a viscous fluid. For the case of an ideal fluid the stability of uniformly accelerated rotations (the Steklov solutions) is studied. A phenomenological model of viscous forces and torques is derived for investigation of the motion in a viscous fluid. A chart of Lyapunov exponents and bifucation diagrams are computed. It is shown that, depending on the system parameters, quasiperiodic and chaotic regimes of motion are possible. Transition to chaos occurs through cascade of period-doubling bifurcations.

Keywords: ideal fluid, viscous fluid, motion of a rigid body, dynamical system, stability of motion, bifurcations, chart of Lyapunov exponents

Funding Agency Grant Number
Russian Foundation for Basic Research 15-08-09093-а
15-38-20879 мол_а_вед
14-01-00395-а


Full text: PDF file (4549 kB)
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Document Type: Article
UDC: 532.3
MSC: 70E15, 65Pxx
Received: 10.02.2016
Revised: 04.03.2016

Citation: V. A. Tenenev, E. V. Vetchanin, L. Ilaletdinov, “Chaotic dynamics in the problem of the fall of a screw-shaped body in a fluid”, Nelin. Dinam., 12:1 (2016), 99–120

Citation in format AMSBIB
\Bibitem{TenVetIla16}
\by V.~A.~Tenenev, E.~V.~Vetchanin, L.~Ilaletdinov
\paper Chaotic dynamics in the problem of the fall of a screw-shaped body in a fluid
\jour Nelin. Dinam.
\yr 2016
\vol 12
\issue 1
\pages 99--120
\mathnet{http://mi.mathnet.ru/nd515}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. E. V. Vetchanin, A. A. Kilin, “Controlled motion of a rigid body with internal mechanisms in an ideal incompressible fluid”, Proc. Steklov Inst. Math., 295 (2016), 302–332  mathnet  crossref  crossref  mathscinet  isi  elib
    2. Evgeny V. Vetchanin, Alexander A. Kilin, Ivan S. Mamaev, “Control of the Motion of a Helical Body in a Fluid Using Rotors”, Regul. Chaotic Dyn., 21:7-8 (2016), 874–884  mathnet  crossref
    3. E. V. Vetchanin, A. A. Kilin, “Upravlenie dvizheniem neuravnoveshennogo tyazhelogo ellipsoida v zhidkosti s pomoschyu rotorov”, Nelineinaya dinam., 12:4 (2016), 663–674  mathnet  crossref  mathscinet  elib
    4. E. V. Vetchanin, V. A. Tenenev, A. A. Kilin, “Optimalnoe upravlenie dvizheniem v idealnoi zhidkosti tela s vintovoi simmetriei s vnutrennimi rotorami”, Kompyuternye issledovaniya i modelirovanie, 9:5 (2017), 741–759  mathnet  crossref
    5. E. V. Vetchanin, A. I. Klenov, “Eksperimentalnye issledovaniya padeniya vintovykh tel v zhidkosti”, Nelineinaya dinam., 13:4 (2017), 585–598  mathnet  crossref  elib
    6. I. S. Mamaev, V. A. Tenenev, E. V. Vetchanin, “Dynamics of a Body with a Sharp Edge in a Viscous Fluid”, Nelineinaya dinam., 14:4 (2018), 473–494  mathnet  crossref
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