Bibliography for the Catenary

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  1. A Generalized Catenary Curve and Simplifying Construction Tasks for Incoming Wires at Transformer Stations
    Sugimoto, S.; Takagi, S.; Fujita, T.; Hata, Y.
    IEEE Pes Transmission and Distribution Conference and Exposition, 2001, vol. 1, pp. 373-378 , Ingenta.  
  2. A catenary problem  
    Lynch, M. A. M.
    Teaching Mathematics and Its Applications, 2001, vol. 20, no. 2, pp. 56-65 , Ingenta.  
  3. The brachistochrone problem with frictional forces.
    Giambò, Roberto; Giannoni, Fabio
    ESAIM Control Optim. Calc. Var. 5 (2000), 187--206 (electronic), Math. Sci. Net.  
  4. Reexamining the Catenary   
    Paul Cella  
    College Math Journal: Volume 30, Number 5, 1999, Pages: 391-393.  
  5. Catenaria vera---the true catenary. Exposition.  
    Denzler, Jochen; Hinz, Andreas M.
    Math. 17 (1999), no. 2, 117--142, Math. Sci. Net.  
  6. Johann Bernoulli's brachistochrone solution using Fermat's principle of least time.
    Erlichson, Herman
    European J. Phys. 20 (1999), no. 5, 299--304, Math. Sci. Net.  
  7. A Catenary Element for the Analysis of Cable Structures.
    Wei, Peng; Bingnan, Sun; Jinchun, Tang
    Applied mathematics and mechanics, 1999, vol. 20, no. 5, pp. 532 , Ingenta.  
  8. Folding pathways as brachistochrones.
    Fernández, Ariel; Niel, Blanca
    Proceedings of the Fourth "Dr. Antonio A. R. Monteiro" Congress on Mathematics (Spanish) (Bahía Blanca, 1997), 179--186, Univ. Nac. del Sur, Bahía Blanca, 1997, Math. Sci. Net.  
  9. Brachistochrone with Coulomb friction.
    Lipp, Stephen C.
    SIAM J. Control Optim. 35 (1997), no. 2, 562--584, Math. Sci. Net.  
  10. A New Minimization Proof for the Brachistochrone  
    Gary Lawlor  
    American Mathematical Monthly, Vol. 103, No. 3. (Mar., 1996), pp. 242-249, Jstor.  
  11. A Note on the Brachistochrone Problem  
    Jim Zeng
    College Math Journal: Volume 27, Number 3, 1996, Pages: 206-208
  12. Exploring the Brachistochrone Problem  
    LaDawn Haws, Terry Kiser  
    American Mathematical Monthly, Vol. 102, No. 4. (Apr., 1995), pp. 328-336, Jstor.  
  13. Finite Catenary and the Method of Lagrange  
    K. Veselic  
    SIAM Review, Vol. 37, No. 2. (Jun., 1995), pp. 224-229, Jstor.  
  14. Optimizing Catenary Length and Tension.
    Machine design, 1995, vol. 67, no. 12, pp. 98 , Ingenta.  
  15. Galileo, Bernoulli, Leibniz and Newton around the brachistochrone problem.
    de Icaza Herrera, Miguel
    Rev. Mexicana Fís. 40 (1994), no. 3, 459--475, Math. Sci. Net.  
  16. A Brief History and Survey of the Catenary Chain Conjectures  
    L. J. Ratliff, Jr.
    American Mathematical Monthly, Vol. 88, No. 3. (Mar., 1981), pp. 169-178, Jstor.  
  17. A new look at the brachistochrone problem.
    van Dooren, René; Vlassenbroeck, Jacques
    Z. Angew. Math. Phys. 31 (1980), no. 6, 785--790, Math. Sci. Net.  
  18. Brachistochrones, tautochrones, evolutes, and tessellations.
    McKinley, John M.
    Amer. J. Phys. 47 (1979), no. 1, 81--86, Math. Sci. Net.  
  19. The brachistochrone for a material point with arbitrary initial velocity.
    Atanackovi'c, T. M.
    Amer. J. Phys. 46 (1978), no. 12, 1274--1275, Math. Sci. Net.  
  20. A Polygonal Arch Generated by Rolling a Polygon (in Classroom Notes)  
    Duane W. DeTemple  
    American Mathematical Monthly, Vol. 82, No. 1. (Jan., 1975), pp. 56-59, Jstor.  
  21. The brachistochrone with acceleration: a running track.
    Drummond, J. E.; Downes, G. L.
    J. Optimization Theory Appl. 7 (1971), 444--449, Math. Sci. Net.  
  22. An Elementary Solution of the Brachistochrone Problem  
    Donald C. Benson  
    American Mathematical Monthly, Vol. 76, No. 8. (Oct., 1969), pp. 890-894, Jstor.  
  23. The Circular Tractrix  
    W. G. Cady  
    American Mathematical Monthly, Vol. 72, No. 10. (Dec., 1965), pp. 1065-1071, Jstor.  
  24. On the Equations for a Flexible Suspension Cable (in Classroom Notes)  
    Morris Morduchow  
    American Mathematical Monthly, Vol. 68, No. 8. (Oct., 1961), pp. 781-783, Jstor.  
  25. The Catenary and the Tractrix (in Classroom Notes)  
    Robert C. Yates
    American Mathematical Monthly, Vol. 66, No. 6. (Jun. - Jul., 1959), pp. 500-505, Jstor.  
  26. Simplified numerical solution of a catenary  
    Geer, Elihu  
    Indust. Math. 7 1956 119--130, Math. Sci. Net.  
  27. Catenary and Tractrix in Non-Euclidean Geometry  
    Fulton, Curtis M.  
    Math. Mag. 27, (1953). 79--84, Math. Sci. Net.  
  28. Discussions: Note on the Catenary (in Questions and Discussions)  
    H. M. Dadourian  
    American Mathematical Monthly, Vol. 31, No. 2. (Feb., 1924), pp. 85-86, Jstor.  
  29. On the Determination of a Catenary with Given Directrix and Passing Through Two Given Points  
    Harris F. MacNeish
    The Annals of Mathematics, 2nd Ser., Vol. 7, No. 2. (Jan., 1906), pp. 65-71, Jstor.  
  30. Concerning The Tractrix of a Curve, with Planimetric Application  
    Derrick N. Lehmer  
    The Annals of Mathematics, 2nd Ser., Vol. 1, No. 1/4. (1899 - 1900), pp. 14-20, Jstor.  
  31. Note on the Catenary  
    W. W. Johnson  
    The Analyst, Vol. 6, No. 4. (Jul., 1879), pp. 119-120, Jstor.  

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2003