Clark, J. D.; Fraser, W. B.; Stump, D. M. Modelling of tension in yarn package unwinding. (English) Zbl 0998.74043 J. Eng. Math. 40, No. 1, 59-75 (2001). From the summary: We present an improved theory for the variation of yarn tension during high speed over-end unwinding from cylindrical yarn packages based upon the theory of bent and twisted elastic rods. A singular perturbation analysis is used to show that the effects of bending and twisting stiffnesses are confined to a boundary layer in the neighbourhood of the unwind point while, over most of the yarn path, the yarn motion can be analyzed with a string theory. The boundary-layer analysis provides a description for the cohesive forces that hold the yarn windings in the package. Cited in 1 Document MSC: 74K10 Rods (beams, columns, shafts, arches, rings, etc.) 74G10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics Keywords:yarn balloons; yarn package unwinding; matched asymptotic expansions; two-timing analysis; elastic rods; singular perturbation analysis; cohesive forces PDFBibTeX XMLCite \textit{J. D. Clark} et al., J. Eng. Math. 40, No. 1, 59--75 (2001; Zbl 0998.74043) Full Text: DOI