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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.

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