Hanging shapes of nonuniform cables

American Journal of Physics

Volumn 65, Issue 2, 1997, Pages 117-122

  Fallis, M C ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0031540133     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.18505     Document Type: Article

References (17)

1. It is assumed that the cable cannot be stretched and offers no resistance to bending.
2. Galileo Galilei, Two New Sciences, Including Centers of Gravity and Forces of Percussion, translated, with Introduction and Notes, by S. Drake (The University of Wisconsin Press, Madison, 1974), p. 143.
3. For a more detailed history, see F. Behroozi, P. Mohazzabi, and J. P. McCrickard, "Remarkable shapes of a catenary under the effect of gravity and surface tension," Am. J. Phys. 62, 1121-1128 (1994).
4. W. W. Rouse Ball, A Short Account of the History of Mathematics (Dover, New York, 1960).
5. For details see, H. H. Goldstine, A History of the Calculus of Variations from the 17th Through the 19th Century (Springer-Verlag, New York, 1980).
6. D. Speiser, Die Streitschriften Von Jacob Und Johann Bernoulli: Variationsrechnung (Birkhäuser, Basel, 1991), p. 503. This reference contains a length introduction (in English) by H. Goldstine followed by reproductions of all the articles (in the original Latin) written by Jacob and Johann Bernoulli on the calculus of variations. Their mathematical notation is translated into modern parlance.
7. H. S. Zapolsky, "A simple solution of the center loaded catenary," Am. J. Phys. 58, 1110-1112 (1990).
8. J. Mathews and R. L. Walker, Mathematical Methods in Physics (Addison-Wesley, Menlo Park, CA, 1970), p. 331.
9. Reference 8, pp. 322-324.
10. I thank Giulio Ruffini for helpful discussion on this subtle point.
11. Reference 6, p. 63.
12. K. R. Symon, Mechanics (Addison, Reading, MA, 1971), p. 241.
13. M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions, 3rd ed. (Dover, New York, 1970), p. 589.
14. W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes in FORTRAN (Cambridge, U.P., Cambridge, U.K., 1992), p. 124. I thank Rodney Glenister for suggesting this approach.
15. Reference 12, p. 257.
16. Reference 12, pp. 239-240.
17. I thank Michael Ashworth for showing me the theta function trick. The same reduction follows less elegantly from integrating by parts.