Pendulum system with an infinite number of equilibrium states and quasiperiodic dynamics

    Received 13 May 2016; accepted 16 May 2016

    2016, Vol. 12, No. 2, pp.  223-234

    Author(s): Kuznetsov A. P., Kuznetsov S. P., Sedova Y. V.

    Examples of mechanical systems are discussed, where quasi-periodic motions may occur, caused by an irrational ratio of the radii of rotating elements that constitute the system. For the pendulum system with frictional transmission of rotation between the elements, in the conservative and dissipative cases we note the coexistence of an infinite number of stable fixed points, and in the case of the self-oscillating system the presence of many attractors in the form of limit cycles and of quasi-periodic rotational modes is observed. In the case of quasi-periodic dynamics the frequencies of spectral components depend on the parameters, but the ratio of basic incommensurate frequencies remains constant and is determined by the irrational number characterizing the relative size of the elements.
    Keywords: dynamic system, mechanical transmission, quasi-periodic oscillations, attractor
    Citation: Kuznetsov A. P., Kuznetsov S. P., Sedova Y. V., Pendulum system with an infinite number of equilibrium states and quasiperiodic dynamics, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 2, pp.  223-234

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