Isoperimetric Inequalities for Moments of Inertia and Stability of Stationary Motions of a Flexible Thread


    2019, Vol. 15, no. 4, pp.  513-523

    Author(s): Kozlov V. V.

    It is well known that the maximal value of the central moment of inertia of a closed homogeneous thread of fixed length is achieved on a curve in the form of a circle. This isoperimetric property plays a key role in investigating the stability of stationary motions of a flexible thread. A discrete variant of the isoperimetric inequality, when the mass of the thread is concentrated in a finite number of material particles, is established. An analog of the isoperimetric inequality for an inhomogeneous thread is proved.
    Keywords: moment of inertia, Sundman and Wirtinger inequalities, articulated polygon
    Citation: Kozlov V. V., Isoperimetric Inequalities for Moments of Inertia and Stability of Stationary Motions of a Flexible Thread, Rus. J. Nonlin. Dyn., 2019, Vol. 15, no. 4, pp.  513-523
    DOI:10.20537/nd190410


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