Isoperimetric inequalities for moments of inertia and stability of stationary motions of a flexible thread. (English) Zbl 1475.53012

Summary: 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.


53A04 Curves in Euclidean and related spaces
49Q10 Optimization of shapes other than minimal surfaces
70C20 Statics
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