Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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The winding of a relaxed elastic line on a cylinder


Author: Gerald S. Manning
Journal: Quart. Appl. Math. 45 (1987), 809-815
MSC: Primary 53A04
DOI: https://doi.org/10.1090/qam/917029
MathSciNet review: 917029
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Abstract: We analyze several cases of the boundary-value problem that determines the path of a relaxed elastic line on a cylinder. A short line with oblique initial tangent deviates from the corresponding helix toward the direction of the axis of the cylinder. A line initially directed along the base circle continues to wind circumferentially if the ratio of its length to the radius of the cylinder does not exceed the critical value $ \pi /{2^{3/2}}$; longer lines deviate from the circle. Infinitely long elastic lines wind in proportion to the logarithm of their arc lengths, as distinct from the direct proportion of a helix. Possible implications for biological structures are discussed.


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DOI: https://doi.org/10.1090/qam/917029
Article copyright: © Copyright 1987 American Mathematical Society


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