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Zbl 0869.73033
Mahadevan, L.; Keller, Joseph B.
Coiling of flexible ropes. (English)
[J] Proc. R. Soc. Lond., Ser. A 452, No.1950, 1679-1694 (1996). ISSN 0080-4630

Summary: A thin flexible inextensible rope fed continuously from a fixed height and falling on a horizontal plane usually forms a circular coil. This phenomenon is analysed as a geometrically nonlinear free-boundary problem for a linearly elastic rope. The stiffness and velocity of the rope, the height from which it is fed and gravity are taken into account. The problem is solved by using a numerical continuation scheme. The coil radius is determined as a function of the various parameters. Tables and graphs are presented.

MSC 2000:: *74K05 Strings

Keywords: dynamic Kirchhoff-Love equations; large bending and twisting deformations; asymptotic solution; geometrically nonlinear free-boundary problems; linearly elastic rope; numerical continuation scheme; coil radius

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