Eugene Kugushev

    Leninskie gory 1, Moscow, 119991, Russia
    Lomonosov Moscow State University


    Kugushev E. I., Popova T. V.
    We consider systems of ordinary differential equations whose right-hand sides contain timeperiodic functions with some frequencies. An averaged system is constructed by introduction of additional variables and by step-by-step averaging over these variables. An upper estimate of the deviation of the solution to the initial system from the solution to the averaged system is given. Examples are given of mechanical systems in which vibrations with several frequencies occur and for the analysis of which the statements obtained are applied.
    Keywords: averaging method, multifrequency perturbations, vibration frequency
    Citation: Kugushev E. I., Popova T. V.,  Estimation of the Accuracy of the Averaging Method for Systems with Multifrequency Perturbations, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 2, pp.  379-394
    Kugushev E. I., Popova T. V.
    The problem of the motion of a homogeneous right circular cylinder with an annular base (a puck) on a horizontal plane with viscous friction is considered. Each point of the base of the puck in contact with the plane is acted upon by the viscous friction force which is proportional to the velocity of this point, and the proportionality coefficient linearly depends on the density of the normal reaction at this point. The density of the normal reaction is determined within the framework of a dynamically consistent model. Some properties of the motion are investigated. In particular, it is shown that for a given direction of the initial angular velocity of the puck, the trajectory of the center of mass of the puck can deviate both to the left and to the right of the straight line directed along the vector of the initial velocity of the center of mass depending on the parameters of the viscous friction model.
    Keywords: puck with annular base, viscous friction, coefficient of friction, dynamically consistent model of normal reactions
    Citation: Kugushev E. I., Popova T. V.,  On the motion of a puck on a horizontal plane in the model of viscous friction with variable coefficient, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 1, pp.  145-153

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