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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
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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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http://mi.mathnet.ru/eng/nd515 http://mi.mathnet.ru/eng/nd/v12/i1/p99
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This publication is cited in the following articles:
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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
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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
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E. V. Vetchanin, A. A. Kilin, “Upravlenie dvizheniem neuravnoveshennogo tyazhelogo ellipsoida v zhidkosti s pomoschyu rotorov”, Nelineinaya dinam., 12:4 (2016), 663–674
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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
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E. V. Vetchanin, A. I. Klenov, “Eksperimentalnye issledovaniya padeniya vintovykh tel v zhidkosti”, Nelineinaya dinam., 13:4 (2017), 585–598
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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
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