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    Evgeny Vetchanin

    Evgeny Vetchanin
    Universitetskaya 1, Izhevsk, 426034 Russia
    Udmurt State University


    Vetchanin  E. V., Gladkov E. S.
    This paper is concerned with the motion of heavy toroidal bodies in a fluid. For experimental purposes, models of solid tori with a width of 3 cm and external diameters of 10 cm, 12 cm and 15 cm have been fabricated by the method of casting chemically solidifying polyurethane (density 1100 kg/m3). Tracking of the models is performed using the underwater Motion Capture system. This system includes 4 cameras, computer and specialized software. A theoretical description of the motion is given using equations incorporating the influence of inertial forces, friction and circulating motion of a fluid through the hole. Values of the model parameters are selected by means of genetic algorithms to ensure an optimal agreement between experimental and theoretical data.
    Keywords: fall through a fluid, torus, body with a hole, multiply connected body, finitedimensional model, object tracking, genetic algorithms
    Citation: Vetchanin  E. V., Gladkov E. S.,  Identification of parameters of the model of toroidal body motion using experimental data, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 1, pp.  99-121
    Vetchanin  E. V., Klenov A. I.
    This paper presents a comparative analysis of computations of the motion of heavy three-bladed screws in a fluid along with experimental results. Simulation of the motion is performed using the theory of an ideal fluid and the phenomenological model of viscous friction. For experimental purposes, models of three-bladed screws with various configurations and sizes were manufactured by casting from chemically hardening polyurethane. Comparison of calculated and experimental results has shown that the mathematical models considered essentially do not reflect the processes observed in the experiments.
    Keywords: motion in a fluid, helical body, experimental investigation
    Citation: Vetchanin  E. V., Klenov A. I.,  Experimental investigation of the fall of helical bodies in a fluid, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 4, pp.  585–598
    Vetchanin  E. V., Kilin A. A.
    This paper is concerned with the motion of an unbalanced heavy three-axial ellipsoid in an ideal fluid controlled by rotation of three internal rotors. It is proved that the motion of the body considered is controlled with respect to configuration variables except for some special cases. An explicit control that makes it possible to implement unbounded motion in an arbitrary direction has been calculated. Directions for which control actions are bounded functions of time have been determined.
    Keywords: ideal fluid, motion of a rigid body, Kirchhoff equations, control by rotors, gaits
    Citation: Vetchanin  E. V., Kilin A. A.,  Control of the motion of an unbalanced heavy ellipsoid in an ideal fluid using rotors, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 4, pp.  663–674
    Tenenev V. A., Vetchanin  E. V., Ilaletdinov L. F.
    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
    Citation: Tenenev V. A., Vetchanin  E. V., Ilaletdinov L. F.,  Chaotic dynamics in the problem of the fall of a screw-shaped body in a fluid, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 1, pp.  99-120
    Kilin A. A., Vetchanin  E. V.
    In this paper we consider the problem of motion of a rigid body in an ideal fluid with two material points moving along circular trajectories. The controllability of this system on the zero level set of first integrals is shown. Elementary “gaits” are presented which allow the realization of the body’s motion from one point to another. The existence of obstacles to a controlled motion of the body along an arbitrary trajectory is pointed out.
    Keywords: ideal fluid, Kirchhoff equations, controllability of gaits
    Citation: Kilin A. A., Vetchanin  E. V.,  The contol of the motion through an ideal fluid of a rigid body by means of two moving masses, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 4, pp.  633–645
    Vetchanin  E. V., Kazakov A. O.
    This paper is concerned with the dynamics of two point vortices of the same intensity which are affected by an acoustic wave. Typical bifurcations of fixed points have been identified by constructing charts of dynamical regimes, and bifurcation diagrams have been plotted.
    Keywords: point vortices, nonintegrability, bifurcations, chart of dynamical regimes
    Citation: Vetchanin  E. V., Kazakov A. O.,  Bifurcations and chaos in the problem of the motion of two point vortices in an acoustic wave, Rus. J. Nonlin. Dyn., 2014, Vol. 10, No. 3, pp.  329-343
    Vetchanin  E. V., Mamaev I. S., Tenenev V. A.
    An investigation of the characteristics of motion of a rigid body with variable internal mass distribution in a viscous fluid is carried out on the basis of a joint numerical solution of the Navier–Stokes equations and equations of motion. A non-stationary three-dimensional solution to the problem is found. The motion of a sphere and a drop-shaped body in a viscous fluid, which is caused by the motion of internal material points, in a gravitational field is explored. The possibility of motion of a body in an arbitrary given direction is shown.
    Keywords: finite-volume numerical method, Navier-Stokes equations, variable internal mass distribution, motion control
    Citation: Vetchanin  E. V., Mamaev I. S., Tenenev V. A.,  The motion of a body with variable mass geometry in a viscous fluid, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 4, pp.  815-836

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