A Falling, Folded String

نویسندگان

  • Kirk T. McDonald
  • Joseph Henry
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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تاریخ انتشار 2017