Evgeny Vetchanin
Universitetskaya 1, Izhevsk, 426034 Russia
Udmurt State University
Publications:
Vetchanin E. V., Portnov E. A.
Construction of Inhomogeneous Velocity Fields Using Expansions in Terms of Eigenfunctions of the Laplace Operator
2022, Vol. 18, no. 3, pp. 441464
Abstract
In this paper we present a method for constructing inhomogeneous velocity fields of an incompressible
fluid using expansions in terms of eigenfunctions of the Laplace operator whose
weight coefficients are determined from the problem of minimizing the integral of the squared
divergence. A number of examples of constructing the velocity fields of planeparallel and axisymmetric
flows are considered. It is shown that the problem of minimizing the integral value
of divergence is incorrect and requires regularization. In particular, we apply Tikhonov’s regularization
method. The method proposed in this paper can be used to generate different initial
conditions in investigating the nonuniqueness of the solution to the Navier – Stokes equations.

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. 507525
Abstract
This paper addresses the problem of balancing an inverted pendulum on an omnidirectional
platform in a threedimensional setting. Equations of motion of the platform – pendulum system
in quasivelocities 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 twodimensional setting is a particular case of threedimensional
balancing.

Vetchanin E. V., Mikishanina E. A.
Vibrational Stability of Periodic Solutions of the Liouville Equations
2019, Vol. 15, no. 3, pp. 351363
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.

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. 4157
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.

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. 473494
Abstract
This paper addresses the problem of planeparallel 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.

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. 99121
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/m^{3}). 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.

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 threebladed 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 threebladed 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.

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 threeaxial 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.

Tenenev V. A., Vetchanin E. V., Ilaletdinov L. F.
Chaotic dynamics in the problem of the fall of a screwshaped body in a fluid
2016, Vol. 12, No. 1, pp. 99120
Abstract
This paper is concerned with the process of the free fall of a threebladed 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 perioddoubling bifurcations.

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.

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. 329343
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.

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. 815836
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 nonstationary threedimensional solution to the problem is found. The motion of a sphere and a dropshaped 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.
