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 Rus. J. Nonlin. Dyn., 2019, Volume 15, Number 4, Pages 513–523 (Mi nd678)

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

V. V. Kozlov

Steklov Mathematical Institute of RAS, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: 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

DOI: https://doi.org/10.20537/nd190410

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MSC: 34D20
Accepted:23.11.2019
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Citation: V. V. Kozlov, “Isoperimetric Inequalities for Moments of Inertia and Stability of Stationary Motions of a Flexible Thread”, Rus. J. Nonlin. Dyn., 15:4 (2019), 513–523

Citation in format AMSBIB
\Bibitem{Koz19} \by V. V. Kozlov \paper Isoperimetric Inequalities for Moments of Inertia and Stability of Stationary Motions of a Flexible Thread \jour Rus. J. Nonlin. Dyn. \yr 2019 \vol 15 \issue 4 \pages 513--523 \mathnet{http://mi.mathnet.ru/nd678} \crossref{https://doi.org/10.20537/nd190410} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=4051667} \elib{https://elibrary.ru/item.asp?id=43289855} \scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85084307599}