Curvature in the equilibrium of a curved elastic wire
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Problem 9.12 from Pólya G., Szegő G. "Problems and Theorems in Analysis" [PóSz98]More problems in Section 9.1 "Some Geometric Problems"
If at every element of a closed, rigid space curve with continuous curvature there acts a force in the direction of the positive principal normal of magnitude , where denotes the radius of curvature, then the curve is in equilibrium.
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Origin: Stated according to the original source
Remark.
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Origin: Stated according to the original source
G. Pólya, problem: Arch. Math. Phys. Ser. 3, 25, p. 337 (1917). Solution by K. Scholl: Arch. Math. Phys. Ser. 3, 28, p. 180 (1920).
References
[PóSz98] Pólya G., Szegő G. Problems and Theorems in Analysis. Springer, 1998.