This paper considers the stability of two planar forms of the elastica: (1) A twisted circular hoop and (2) the classical noninflectional plane elastica. By means of the Kirchhoff thin-rod theory, the critical loads at which the planar forms become unstable and tend to “pop out” into spatial forms are determined. The results are related to the problems of coiling and kinking of submarine cable.
Stability of Two Planar Loop Elasticas
E. E. Zajac
Bell Telephone Laboratories, Inc., Murray Hill, N. J.
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Zajac, E. E. (March 1, 1962). "Stability of Two Planar Loop Elasticas." ASME. J. Appl. Mech. March 1962; 29(1): 136–142. https://doi.org/10.1115/1.3636445
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