A Particle on a Moving Plane with Coulomb Friction

    Received 30 June 2019

    2019, Vol. 15, no. 3, pp.  343-349

    Author(s): Zubelevich O. E.

    This paper is concerned with the motion of a particle on a horizontal vibrating plane with Coulomb friction. It is proved that, when some constant force is added, the system has a periodic solution.
    Keywords: classical mechanics, systems with friction, Filippov’s systems, periodic solutions, differential inclusions
    Citation: Zubelevich O. E., A Particle on a Moving Plane with Coulomb Friction, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 3, pp.  343-349
    DOI:10.20537/nd190311


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    References

    [1] Benedetti, A., Sornay, P., Dalloz, B., and Nicolas, M., “Angular Particle Sliding Down a Transversally Vibrated Smooth Plane”, Phys. Rev. E, 85:1, 1 (2012), 011307, 8 pp.  crossref  adsnasa
    [2] Agarwal, R., Meehan, M., and O'Regan, D., Fixed Point Theory and Applications, Cambridge Tracts in Math., 141, Cambridge Univ. Press, Cambridge, 2001, 170 pp.  mathscinet  zmath  adsnasa
    [3] Blekhman, I. I., Vibrational Mechanics: Nonlinear Dynamic Effects, General Approach, Applications, World Sci., River Edge, N.J., 2000, 536 pp.  mathscinet
    [4] Joukovsky, N. E., “Note on a flat sifter screen”, Collected Papers, v. 8, Theory of Elasticity, Railways, Automobiles, ed. A. P. Kotelnikov, Gostekhizdat, Moscow, 1937, 39–46 (Russian)
    [5] Filippov, A. F., “Differential Equations with Discontinuous Right-Hand Side”, Mat. Sb. (N. S.), 51(93):1 (1960), 99–128 (Russian)  mathnet  mathscinet  zmath
    [6] Filippov, A. F., Differential Equations with Discontinuous Righthand Sides, Math. Appl., 18, Springer, Dordrecht, 1988, X, 304 pp.  mathscinet
    [7] Schwartz, L., Cours d'analyse, v. 2, Hermann, Paris, 1967, 571 pp.  mathscinet



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