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2013
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    Alexandr Kuleshov

    Moscow, 119899, Vorobievy gory
    Departament of Mechanics and Mathematics Moscow State University

    Publications:

    Kuleshov A. S., Hubbard M., Peterson D. L., Gede G.
    Motion of the oloid on the horizontal plane
    2011, Vol. 7, No. 4, pp.  825-835
    Abstract
    We present a kinematic analysis and numerical simulation of the toy known as the oloid. The oloid is defined by the convex hull of two equal radius disks whose symmetry planes are at right angles with the distance between their centers equal to their radius. The no-slip constraints of the oloid are integrable, hence the system is essentially holonomic. In this paper we present analytic expressions for the trajectories of the ground contact points, basic dynamic analysis, and observations on the unique behavior of this system.
    Keywords: oloid, rolling motion, holonomic system, kinematics
    Citation: Kuleshov A. S., Hubbard M., Peterson D. L., Gede G.,  Motion of the oloid on the horizontal plane, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 4, pp.  825-835
    DOI:10.20537/nd1104006
    Kuleshov A. S., Treschev D. V., Ivanova T. B., Naymushina O. S.
    A rigid cylinder on a viscoelastic plane
    2011, Vol. 7, No. 3, pp.  601-625
    Abstract
    The paper considers two two-dimensional dynamical problems for an absolutely rigid cylinder interacting with a deformable flat base (the motion of an absolutely rigid disk on a base which in non-deformed condition is a straight line). The base is a sufficiently stiff viscoelastic medium that creates a normal pressure $p(x) = kY(x)+ν\dot{Y}(x)$, where $x$ is a coordinate on the straight line, $Y(x)$ is a normal displacement of the point $x$, and $k$ and $ν$ are elasticity and viscosity coefficients (the Kelvin—Voigt medium). We are also of the opinion that during deformation the base generates friction forces, which are subject to Coulomb’s law. We consider the phenomenon of impact that arises during an arbitrary fall of the disk onto the straight line and investigate the disk’s motion «along the straight line» including the stages of sliding and rolling.
    Keywords: Kelvin–Voight medium, impact, viscoelasticity, friction
    Citation: Kuleshov A. S., Treschev D. V., Ivanova T. B., Naymushina O. S.,  A rigid cylinder on a viscoelastic plane, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 3, pp.  601-625
    DOI:10.20537/nd1103014
    Kremnev A. V., Kuleshov A. S.
    Nonlinear Dynamics of a Simplified Skateboard Model
    2008, Vol. 4, No. 3, pp.  323-340
    Abstract
    Analysis and simulation are performed for a simplifiedmodel of a skateboard in the absence of rider control. Equations of motion of the model are derived and the problem of integrability of the obtained equations is investigated. The influence of various parameters of the model on its dynamics and stability are studied.
    Keywords: skateboard, nonholonomic constraints, integrability, stability of motion
    Citation: Kremnev A. V., Kuleshov A. S.,  Nonlinear Dynamics of a Simplified Skateboard Model, Rus. J. Nonlin. Dyn., 2008, Vol. 4, No. 3, pp.  323-340
    DOI:10.20537/nd0803006
    Kremnev A. V., Kuleshov A. S.
    Abstract
    In this paper we continue our investigation of dynamics and stability of motion of a skateboard with a rider. In our previous papers we assumed that the rider, modeled as a rigid body, remains fixed and perpendicular with respect to the board. Hence if the board tilts through γ, the rider tilts through the same angle relative to the vertical, i. e. only one generalized coordinate γ describes the tilt of the board and rider.
    Now we make the next step in modeling complexity and we allow the board and rider to have separate degrees of freedom, γ and φ, respectively. Here the rider is assumed to be connected to the board with a pin along the central line of the board through a torsional spring which exerts a torque on the rider and board proportional to the difference in their tilts relative to the vertical. Equations of motion of the model are derived and the problem of integrability of the obtained equations is investigated. The influence of various parameters of the model on its dynamics and stability is studied.
    Keywords: skateboard, nonholonomic constraints, integrability, stability of motion
    Citation: Kremnev A. V., Kuleshov A. S.,  Nonlinear Dynamics of a Skateboard Model with Three Degrees of Freedom, Rus. J. Nonlin. Dyn., 2008, Vol. 4, No. 3, pp.  341-355
    DOI:10.20537/nd0803007

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