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2013
Impact Factor

    Olga Naymushina

    1, Universitetskaya str., Izhevsk, 426034, Russia
    osn@rcd.ru
    Udmurt State University

    Publications:

    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
    Vaskin V. V., Naymushina O. S.
    Abstract
    The motion without bouncing (i.e. in constant contact) of a certain model of a nonhomogeneous ball on a smooth plane is considered. The dependance of the domains of such motion on the shift of the center mass in the space of integrals of motion is analyzed.
    Keywords: rigid body, motion without bouncing on a smooth plane
    Citation: Vaskin V. V., Naymushina O. S.,  On the motion of a ball without bouncing on a smooth plane: II, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 4, pp.  823-828
    DOI:10.20537/nd1004007
    Vaskin V. V., Naymushina O. S.
    Abstract
    We analyze domains of an axisymmetric ball with the shifted center mass motion without bouncing (i. e. in constant contact) on a smooth plane. We show that these domains belong to the region of parameters, corresponding to regimes of regular precession (the ball’s axis about axis z). We also give explicit formulas for domain boundaries.
    Keywords: rigid body, motion without bouncing on a smooth plane
    Citation: Vaskin V. V., Naymushina O. S.,  On the motion of a ball without bouncing on a smooth plane, Rus. J. Nonlin. Dyn., 2009, Vol. 5, No. 4, pp.  625-632
    DOI:10.20537/nd0904013

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