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
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.
moment of inertia, Sundman and Wirtinger inequalities, articulated polygon
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V. V. Kozlov, “Isoperimetric Inequalities for Moments of Inertia and Stability of Stationary Motions of a Flexible Thread”, Nelin. Dinam., 15:4 (2019), 513–523
Citation in format AMSBIB
\by V. V. Kozlov
\paper Isoperimetric Inequalities for Moments of Inertia and Stability of Stationary Motions of a Flexible Thread
\jour Nelin. Dinam.
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