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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
Received: 24.07.2019
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}


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