Geodesic
Isoperimetric Inequalities for Moments of Inertia and Stability of Stationary Motions of a Flexible Thread
Russian journal of nonlinear dynamics, Tome 15 (2019) no. 4, pp. 513-523

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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: Sundman and Wirtinger inequalities, articulated polygon.
Mots-clés : moment of inertia 
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     author = {V. V. Kozlov},
     title = {Isoperimetric {Inequalities} for {Moments} of {Inertia} and {Stability} of {Stationary} {Motions} of a {Flexible} {Thread}},
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V. V. Kozlov. Isoperimetric Inequalities for Moments of Inertia and Stability of Stationary Motions of a Flexible Thread. Russian journal of nonlinear dynamics, Tome 15 (2019) no. 4, pp. 513-523. http://geodesic.mathdoc.fr/item/ND_2019_15_4_a10/