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2013
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# Evgeny Vetchanin Universitetskaya 1, Izhevsk, 426034 Russia
Udmurt State University

## Publications:

 Shaura A. S., Tenenev V. A., Vetchanin E. V. The Problem of Balancing an Inverted Spherical Pendulum on an Omniwheel Platform 2021, Vol. 17, no. 4, pp.  507-525 Abstract This paper addresses the problem of balancing an inverted pendulum on an omnidirectional platform in a three-dimensional setting. Equations of motion of the platform – pendulum system in quasi-velocities are constructed. To solve the problem of balancing the pendulum by controlling the motion of the platform, a hybrid genetic algorithm is used. The behavior of the system is investigated under different initial conditions taking into account a necessary stop of the platform or the need for continuation of the motion at the end point of the trajectory. It is shown that the solution of the problem in a two-dimensional setting is a particular case of three-dimensional balancing. Keywords: balancing of an inverted pendulum, omnidirectional platform, hybrid genetic algorithm, Poincaré equations in quasi-velocities Citation: Shaura A. S., Tenenev V. A., Vetchanin E. V.,  The Problem of Balancing an Inverted Spherical Pendulum on an Omniwheel Platform, Rus. J. Nonlin. Dyn., 2021, Vol. 17, no. 4, pp.  507-525 DOI:10.20537/nd210411
 Vetchanin E. V., Mikishanina E. A. Vibrational Stability of Periodic Solutions of the Liouville Equations 2019, Vol. 15, no. 3, pp.  351-363 Abstract The dynamics of a body with a fixed point, variable moments of inertia and internal rotors are considered. A stability analysis of permanent rotations and periodic solutions of the system is carried out. In some simplest cases the stability analysis is reduced to investigating the stability of the zero solution of Hill’s equation. It is shown that by periodically changing the moments of inertia it is possible to stabilize unstable permanent rotations of the system. In addition, stable dynamical regimes can lose stability due to a parametric resonance. It is shown that, as the oscillation frequency of the moments of inertia increases, the dynamics of the system becomes close to an integrable one. Keywords: Liouville equations, Euler –Poisson equations, Hill’s equation, Mathieu equation, parametric resonance, vibrostabilization, Euler – Poinsot case, Joukowski –Volterra case Citation: Vetchanin E. V., Mikishanina E. A.,  Vibrational Stability of Periodic Solutions of the Liouville Equations, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 3, pp.  351-363 DOI:10.20537/nd190312
 Vetchanin E. V. The Motion of a Balanced Circular Cylinder in an Ideal Fluid Under the Action of External Periodic Force and Torque 2019, Vol. 15, no. 1, pp.  41-57 Abstract The motion of a circular cylinder in a fluid in the presence of circulation and external periodic force and torque is studied. It is shown that for a suitable choice of the frequency of external action for motion in an ideal fluid the translational velocity components of the body undergo oscillations with increasing amplitude due to resonance. During motion in a viscous fluid no resonance arises. Explicit integration of the equations of motion has shown that the unbounded propulsion of the body in a viscous fluid is impossible in the absence of external torque. In the general case, the solution of the equations is represented in the form of a multiple series. Keywords: rigid body dynamics, ideal fluid, viscous fluid, propulsion in a fluid, resonance Citation: Vetchanin E. V.,  The Motion of a Balanced Circular Cylinder in an Ideal Fluid Under the Action of External Periodic Force and Torque, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 1, pp.  41-57 DOI:10.20537/nd190105
 Mamaev I. S., Tenenev V. A., Vetchanin E. V. Dynamics of a Body with a Sharp Edge in a Viscous Fluid 2018, Vol. 14, no. 4, pp.  473-494 Abstract This paper addresses the problem of plane-parallel motion of the Zhukovskii foil in a viscous fluid. Various motion regimes of the foil are simulated on the basis of a joint numerical solution of the equations of body motion and the Navier – Stokes equations. According to the results of simulation of longitudinal, transverse and rotational motions, the average drag coefficients and added masses are calculated. The values of added masses agree with the results published previously and obtained within the framework of the model of an ideal fluid. It is shown that between the value of circulation determined from numerical experiments, and that determined according to the model of and ideal fluid, there is a correlation with the coefficient $\mathcal{R} = 0.722$. Approximations for the lift force and the moment of the lift force are constructed depending on the translational and angular velocity of motion of the foil. The equations of motion of the Zhukovskii foil in a viscous fluid are written taking into account the found approximations and the drag coefficients. The calculation results based on the proposed mathematical model are in qualitative agreement with the results of joint numerical solution of the equations of body motion and the Navier – Stokes equations. Keywords: Zhukovskii foil, Navier – Stokes equations, joint solution of equations, finitedimensional model, viscous fluid, circulation, sharp edge Citation: Mamaev I. S., Tenenev V. A., Vetchanin E. V.,  Dynamics of a Body with a Sharp Edge in a Viscous Fluid, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 4, pp.  473-494 DOI:10.20537/nd180404
 Vetchanin E. V., Gladkov E. S. Identification of parameters of the model of toroidal body motion using experimental data 2018, Vol. 14, no. 1, pp.  99-121 Abstract 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 DOI:10.20537/nd1801009
 Vetchanin E. V., Klenov A. I. Experimental investigation of the fall of helical bodies in a fluid 2017, Vol. 13, No. 4, pp.  585–598 Abstract 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 DOI:10.20537/nd1704011
 Vetchanin E. V., Kilin A. A. Control of the motion of an unbalanced heavy ellipsoid in an ideal fluid using rotors 2016, Vol. 12, No. 4, pp.  663–674 Abstract 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 DOI:10.20537/nd1604009
 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 2016, Vol. 12, No. 1, pp.  99-120 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 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 DOI:10.20537/nd1601007
 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 2015, Vol. 11, No. 4, pp.  633–645 Abstract 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 DOI:10.20537/nd1504001
 Vetchanin E. V., Kazakov A. O. Bifurcations and chaos in the problem of the motion of two point vortices in an acoustic wave 2014, Vol. 10, No. 3, pp.  329-343 Abstract 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 DOI:10.20537/nd1403007
 Vetchanin E. V., Mamaev I. S., Tenenev V. A. The motion of a body with variable mass geometry in a viscous fluid 2012, Vol. 8, No. 4, pp.  815-836 Abstract 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 DOI:10.20537/nd1204010