Elizaveta Artemova

    Elizaveta Artemova
    ul. Universitetskaya 1, Izhevsk, 426034 Russia
    Udmurt State University


    Kilin A. A., Artemova E. M.
    This paper addresses the problem of the motion of two point vortices of arbitrary strengths in an ideal incompressible fluid on a finite flat cylinder. A procedure of reduction to the level set of an additional first integral is presented. It is shown that, depending on the parameter values, three types of bifurcation diagrams are possible in the system. A complete bifurcation analysis of the system is carried out for each of them. Conditions for the orbital stability of generalizations of von Kármán streets for the problem under study are obtained.
    Keywords: point vortices, ideal fluid, flat cylinder, bifurcation diagram, phase portrait, von Kármán vortex street, stability, boundary, flow in a strip
    Citation: Kilin A. A., Artemova E. M.,  Bifurcation Analysis of the Problem of Two Vortices on a Finite Flat Cylinder, Rus. J. Nonlin. Dyn., 2024, Vol. 20, no. 1, pp.  95-111
    Artemova E. M., Kilin A. A.
    This paper is concerned with the controlled motion of a three-link wheeled snake robot propelled by changing the angles between the central and lateral links. The limits on the applicability of the nonholonomic model for the problem of interest are revealed. It is shown that the system under consideration is completely controllable according to the Rashevsky – Chow theorem. Possible types of motion of the system under periodic snake-like controls are presented using Fourier expansions. The relation of the form of the trajectory in the space of controls to the type of motion involved is found. It is shown that, if the trajectory in the space of controls is centrally symmetric, the robot moves with nonzero constant average velocity in some direction.
    Keywords: nonholonomic mechanics, wheeled vehicle, snake robot, controllability, periodic control
    Citation: Artemova E. M., Kilin A. A.,  A Nonholonomic Model and Complete Controllability of a Three-Link Wheeled Snake Robot, Rus. J. Nonlin. Dyn., 2022, Vol. 18, no. 4, pp.  681-707

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