A Falling, Folded String
نویسندگان
چکیده
This classic problem was brought to the author’s attention by Johann Otto. This view seems to be advocated by Routh (1896) in Ex. 4, p. 82 of [13]. Examples of falling chains were often considered at Cambridge U. [11, 12, 13, 14, 16, 18, 19], as recounted in a footnote on p. 80 of [13]: Problems on infinitesimal impulses were solved in the lecture room of the late Mr Hopkins as long ago as 1850. A problem of this kind was set in the Smith’s Prize examination in 1853 by Prof Challis, and a solution given in Tait and Steele’s Dynamics. For the latter, see pp. 250-251 of [5]. The earliest example of a variable-mass string problem may be due to Buquoy (1815) [3, 62, 87], to which the only published reference in the 19 century was by Poisson (1819) [4]. Also of note in the 19 century are papers by Cayley [6, 9], and those related to the laying of the transAtlantic cable [7, 8]. The latter activity includes the interesting phenomena of vertical “arching” as a slack string is pulled from a nominally horizontal configuration at rest [72, 81], which has led to the fascinating “chain fountain” [76, 77, 78, 82, 84, 86]. Variable-mass problems involving jets were first considered by Bernoulli (1738) [1], and perhaps next by Moore (1813) [2]. A paper by de Mondesir (1887) [10] on variable-mass systems involving chains led to some debate, later discussed in [15].
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