On the Motion of a Body with a Moving Internal Mass on a Rough Horizontal Plane

    Received 16 August 2018; accepted 24 August 2018

    2018, Vol. 14, no. 4, pp.  519-542

    Author(s): Bardin B. S., Panev A. S.

    We consider a vibration-driven system which consists of a rigid body and an internal mass. The internal mass is a particle moving in a circle inside the body. The center of the circle is located at the mass center of the body and the absolute value of particle velocity is a constant. The body performs rectilinear motion on a horizontal plane, whereas the particle moves in a vertical plane. We suppose that dry friction acts between the plane and the body.
    We have investigated the dynamics of the above system in detail and given a full description of the body’s motion for any values of its initial velocity. In particular, it is shown that there always exists a periodic mode of motion. Depending on parameter values, one of three types of this periodic mode takes place. At any initial velocity the body either enters a periodic mode during a finite time interval or it asymptotically approaches the periodic mode.
    Keywords: periodic motion, dry friction, rigid body, vibration-driven system
    Citation: Bardin B. S., Panev A. S., On the Motion of a Body with a Moving Internal Mass on a Rough Horizontal Plane, Rus. J. Nonlin. Dyn., 2018, Vol. 14, no. 4, pp.  519-542
    DOI:10.20537/nd180407


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