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2013
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    Alexander Baikov

    Moscow Aviation Institute

    Publications:

    Baikov A., Kovalev N.
    Abstract
    The motion of a piecewise linear oscillator is considered. It consists of two spring connected drawers on a conveyor belt moving at a constant speed. The equations of motion are averaged in one nonresonance case. A continuum of invariant tori is obtained that exists in the exact system. The attraction (in finite time) of the trajectories to the family of limit tori is proved (limit tori belong to the continuum of invariant tori). We also investigate zones of sticking, which cannot be detected by averaging.
    Keywords: equations with discontinuities, piecewise linear oscillator, averaging method, invariant torus, sticking zone
    Citation: Baikov A., Kovalev N.,  Investigation of the dynamics of a two-degrees-of-freedom piecewise linear oscillator, Rus. J. Nonlin. Dyn., 2017, Vol. 13, No. 4, pp.  533–542
    DOI:10.20537/nd1704006
    Baikov A., Mayorov A. Y.
    Abstract
    The destabilization of the stable equilibrium position of a non-conservative system with three degrees of freedom under the action of a linear viscous friction force is considered. The dissipation is assumed to be completed. The standard methods of the stability theory are using for solving problem. Stability of equilibrium position is studied in the linear approximation. The coefficients of characteristic polynomial are constructed by using Le Verrier’s algorithm. Ziegler’s effect condition and criterion for the stability are constructed by using perturbation theory. Stability of the three-link rod system’s equilibrium position is investigated, when there is no dissipative force. Ziegler’s area and criterion for the stability of the equilibrium position of a system with three degrees of freedom, in which the friction forces take small values, are constructed. The influence of large friction forces is investigated. The results of the study may be used for the analysis of stability of a non-conservative system with three degrees of freedom. Also, the threelink rod system may be used as discrete model of filling hose under the action of reactive force.
    Keywords: fillling hose, discrete model, three-link rod system, tracking force, dissipative forces, asymptotically stability, Ziegler’s effect, Ziegler’s areas, criterion for the stability
    Citation: Baikov A., Mayorov A. Y.,  On the equilibrium position stability of discrete model of filling hose under the action of reactive force, Rus. J. Nonlin. Dyn., 2015, Vol. 11, No. 1, pp.  127-146
    DOI:10.20537/nd1501007

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