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    Victor Zhuravlev

    pr. Vernadskogo, 101, block 1, Moscow, 119526, Russia
    A. Ishlinsky Institite for Problems in Mechanics, RAS


    Zhuravlev V. F., Rozenblat G. M.
    This paper presents secure upper and lower estimates for solutions to the equations of rigid body motion in the Euler case (in the absence of external torques). These estimates are expressed by simple formulae in terms of elementary functions and are used for solutions that are obtained in a neighborhood of the unstable steady rotation of the body about its middle axis of inertia. The estimates obtained are applied for a rigorous explanation of the flip-over phenomenon which arises in the experiment with Dzhanibekov’s nut.
    Keywords: Euler top, permanent (steady) rotation, middle axis of inertia, estimates of solutions to differential equations
    Citation: Zhuravlev V. F., Rozenblat G. M.,  Estimates of Solutions During Motion of the Euler –Poinsot Top and Explanation of the Experiment with Dzhanibekov’s Nut, Rus. J. Nonlin. Dyn., 2020, Vol. 16, no. 3, pp.  517-525
    Zhuravlev V. F.
    Van der Pol’s controlled 2D oscillator
    2016, Vol. 12, No. 2, pp.  211-222
    There are two reasons for 2D auto-oscillations to be of such interest for analysis. Firstly, mechanical systems based on such a model are widely used. Secondly, unlike 1D van der Pol’s oscillator, a 2D model as a mathematical object has much more characteristics: in addition to potential and dissipative forces, more complicated forces can be taken into account, which characterize different specific behaviors of the oscillator.
    Keywords: van der Pol’s oscillator
    Citation: Zhuravlev V. F.,  Van der Pol’s controlled 2D oscillator, Rus. J. Nonlin. Dyn., 2016, Vol. 12, No. 2, pp.  211-222
    Zhuravlev V. F.
    Notion of constraint in analytical mechanics
    2012, Vol. 8, No. 4, pp.  853-860
    A critical review of such notions as holonomic and non-holonomic, unilateral and binary constraints is given. The correctness of these models is considered.
    Citation: Zhuravlev V. F.,  Notion of constraint in analytical mechanics, Rus. J. Nonlin. Dyn., 2012, Vol. 8, No. 4, pp.  853-860
    Zhuravlev V. F.
    Citation: Zhuravlev V. F.,  Comments on "Lagrangian mechanics and dry friction" by V. V. Kozlov, Rus. J. Nonlin. Dyn., 2011, Vol. 7, No. 1, pp.  147-149
    Zhuravlev V. F.
    Reply to A. V. Borisov
    2010, Vol. 6, No. 3, pp.  671-674
    Citation: Zhuravlev V. F.,  Reply to A. V. Borisov, Rus. J. Nonlin. Dyn., 2010, Vol. 6, No. 3, pp.  671-674

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