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2013
Impact Factor

Evgeny Vetchanin

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

Publications:

Vetchanin  E. V., Mamaev I. S.
Dynamics of Two Point Vortices in an External Compressible Shear Flow
2017, vol. 22, no. 8, pp.  893–908
Abstract
This paper is concerned with a system of equations that describes the motion of two point vortices in a flow possessing constant uniform vorticity and perturbed by an acoustic wave. The system is shown to have both regular and chaotic regimes of motion. In addition, simple and chaotic attractors are found in the system. Attention is given to bifurcations of fixed points of a Poincar´e map which lead to the appearance of these regimes. It is shown that, in the case where the total vortex strength changes, the “reversible pitch-fork” bifurcation is a typical scenario of emergence of asymptotically stable fixed and periodic points. As a result of this bifurcation, a saddle point, a stable and an unstable point of the same period emerge from an elliptic point of some period. By constructing and analyzing charts of dynamical regimes and bifurcation diagrams we show that a cascade of period-doubling bifurcations is a typical scenario of transition to chaos in the system under consideration.
Keywords: point vortices, shear flow, perturbation by an acoustic wave, bifurcations, reversible pitch-fork, period doubling
Citation: Vetchanin  E. V., Mamaev I. S.,  Dynamics of Two Point Vortices in an External Compressible Shear Flow, Regular and Chaotic Dynamics, 2017, vol. 22, no. 8, pp. 893–908
DOI:10.1134/S1560354717080019
Vetchanin  E. V., Kilin A. A., Mamaev I. S.
Control of the Motion of a Helical Body in a Fluid Using Rotors
2016, vol. 21, no. 7-8, pp.  874-884
Abstract
This paper is concerned with the motion of a helical body in an ideal fluid, which is controlled by rotating three internal rotors. It is proved that the motion of the body is always controllable by means of three rotors with noncoplanar axes of rotation. A condition whose satisfaction prevents controllability by means of two rotors is found. Control actions that allow the implementation of unbounded motion in an arbitrary direction are constructed. Conditions under which the motion of the body along an arbitrary smooth curve can be implemented by rotating the rotors are presented. For the optimal control problem, equations of sub-Riemannian geodesics on $SE(3)$ are obtained.
Keywords: ideal fluid, motion of a helical body, Kirchhoff equations, control of rotors, gaits, optimal control
Citation: Vetchanin  E. V., Kilin A. A., Mamaev I. S.,  Control of the Motion of a Helical Body in a Fluid Using Rotors, Regular and Chaotic Dynamics, 2016, vol. 21, no. 7-8, pp. 874-884
DOI:10.1134/S1560354716070108
Vetchanin  E. V., Mamaev I. S., Tenenev V. A.
The Self-propulsion of a Body with Moving Internal Masses in a Viscous Fluid
2013, vol. 18, no. 1-2, pp.  100-117
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 for a rigid body. A nonstationary three-dimensional solution to the problem is found. The motion of a sphere and a drop-shaped body in a viscous fluid in a gravitational field, which is caused by the motion of internal material points, is explored. The possibility of self-propulsion 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 Self-propulsion of a Body with Moving Internal Masses in a Viscous Fluid, Regular and Chaotic Dynamics, 2013, vol. 18, no. 1-2, pp. 100-117
DOI:10.1134/S1560354713010073

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