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Field Theory Handbook pp 77–95Cite as

Cylindrical Systems

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Abstract

The cylindrical coordinate systems are obtained by translating each of the maps, Figs. 2.01 to 2.21, in a direction perpendicular to the graphs, thus forming two orthogonal families of cylinders. The third family of coordinate surfaces consists of parallel planes, z = const. The coordinate axis that is parallel to the generators of the cylinders is called the z-axis in all cases.

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Bibliography

  1. Klein, F.: Vorlesungen über lineare Differentialgleichungen der zweiten Ordnung. Göttingen: E. Ritter 1894.

    Google Scholar 

  2. Casey, M.: On cyclides and sphero-quartics. Phil. Trans. Roy. Soc. Lond. 161, 585 (1871).

    Article  MATH  Google Scholar 

  3. Darboux, G.: Remarques sur la théorie des surfaces orthogonales. C. R. Acad. Sci., Paris 59, 240 (1864).

    Google Scholar 

  4. Darboux, G.: Sur l’application des méthodes dc la physique mathématique à l’étude des corps terminés par des cyclides. C. R. Acad. Sci., Paris 83, 1037, 1099 (1876).

    Google Scholar 

  5. Maxwell, J. C.: On the cyclide. Quart. J. Math. 9, 111 (1868).

    Google Scholar 

  6. Coolidge, J. L.: A treatise on the circle and the sphere. London: Oxford Univ. Press 1916.

    Google Scholar 

  7. Darboux, G.: Leçons sur les systèmes orthogonaux et les coordonnées curvilignes, p. 277. Paris: Gauthier-Villars 1910.

    Google Scholar 

  8. Jeans, J. H.: Electricity and magnetism. Cambridge: Cambridge Univ. Press 1925.

    Google Scholar 

  9. Maxwell, J. C.: Electricity and magnetism. London: Oxford Univ. Press 1904.

    Google Scholar 

  10. Schmidt, H.: Die Inversion und ihre Anwendung. München: R. Oldenbourg 1950.

    Google Scholar 

  11. Thomson, W.: Extrait d’un lettre à M. LIOUVILLE. J. Math. pures appl. 10,364 (1845). (The first use of inversion in electrostatics.)

    Google Scholar 

  12. Thomson, W.: Extraits de deuxlettres adressées à M. LIOUVILLE. J. Math. pures appl. 12, 256 (1847).

    Google Scholar 

  13. Liouville, J.: Note au sujet de l’article précédent. J. Math. pures appl. 12, 265 (1847).

    Google Scholar 

  14. Thompson, W., and P. G. TAIT: Treatise on natural philosophy, Part II, p. 62. Cambridge: Cambridge Univ. Press 1890.

    Google Scholar 

  15. Wangerin, A.: Theorie des Potentials und der Kugelfunktionen, Bd. II, S. 147. Berlin: Walter de Gruyter 1921.

    Google Scholar 

  16. Weber, E.: Electromagnetic fields, p. 244. New York: John Wiley & Sons 1950.

    Google Scholar 

  17. Wrinch, D. M.: Inverted prolate spheroids. Phil. Mag. 14, 1061 (1932).

    Google Scholar 

  18. Moon, P., and D. E. SPENCER: Cylindrical and rotational coordinate systems. J. Franklin Inst. 252, 327 (1951).

    Article  MathSciNet  Google Scholar 

  19. Moon, P., and D. E. SPENCER: Some coordinate systems associated with elliptic functions. J. Franklin Inst. 255, 531 (1953).

    Article  MathSciNet  Google Scholar 

  20. Churchill, R. V.: Complex variables and applications. New York: McGraw-Hill Book Co. 1960.

    MATH  Google Scholar 

  21. Knopp, K.: Theory of functions. New York: Dover Publications 1945.

    Google Scholar 

  22. Nehari, Z.: Conformal mapping. New York: McGraw-Hill Book Co. 1952.

    MATH  Google Scholar 

  23. Osgood, W. F.: Lehrbuch der Funktionentheorie. Leipzig: B. G. Teubner 1928.

    Google Scholar 

  24. Rothe, R., F. OLLENDORFF and K. POHLHAUSEN: Theory of functions. Cambridge, Mass.: Technology Press 1933.

    Google Scholar 

  25. Titchmarsh, E. C.: Theory of functions. London: Oxford Univ. Press 1932.

    Google Scholar 

  26. Townsend, E. J.: Functions of a complex variable. New York: Henry Holt & Co. 1915.

    Google Scholar 

  27. Walker, M.: Conjugate functions for engineers. London: Oxford Univ. Press 1933.

    Google Scholar 

  28. Kober, H.: Dictionary of conformal representations. New York: Dover Publications 1952.

    MATH  Google Scholar 

  29. Love, A. E. H.: Some electrostatic distributions in two dimensions. Proc. London Math. Soc. 22, 337 (1924).

    MATH  Google Scholar 

  30. Michell, J. H.: A map of the complex Z-function: a condenser problem. Messenger of Math. 23, 72 (1894).

    Google Scholar 

  31. Greenhill, G.: Theory of a stream line past a plane barrier. Advisory Comm. for Aeronautics, Report No. 19, London 1910.

    Google Scholar 

  32. Applications of complex transformations

    Google Scholar 

  33. Andronescu, P.: Das parallel- und meridianebene Feld nebst Beispielen. Arch. Elektrotechn. 14, 379 (1924).

    Article  Google Scholar 

  34. Bairstow, L.: Resistance of a cylinder moving in a viscous fluid. Phil. Trans. Roy. Soc. Lond. 223, 383 (1923).

    Article  ADS  MATH  Google Scholar 

  35. Glauert, H.: Elements of aerofoil and airscrew theory. Cambridge: Cambridge Univ. Press 1926.

    Google Scholar 

  36. GrÖsser, W.: Einige elektrostatische Probleme der Hochspannungstechnik. Arch. Elektrotechn. 25, 193 (1931).

    Article  MATH  Google Scholar 

  37. HoltzmÜller, O.: Über die logarithmische Abbildung und die aus ihr entspringenden orthogonalen Kurvensysteme. Z. Math. Phys. 16, 269 (1871).

    Google Scholar 

  38. Beiträge zur Theorie der isogonalen Verwandtschaften. Z. Math. Phys. 18, 227 (1873).

    Google Scholar 

  39. HoltzmÜller, O.: Weitere Beiträge zur Theorie der isogonalen Verwandtschaften. Z. Math. Phys. 20, 1 (1875).

    Google Scholar 

  40. HoltzmÜller, O.: Einführung in die Theorie der isogonalen Verwandtschaften. Leipzig: B. G. Teubner 1882.

    Google Scholar 

  41. Kehren, E.: Anwendung der konformen Abbildung in der Elektrostatik. Ann. d. Phys. 14, 367 (1932).

    Article  ADS  Google Scholar 

  42. Knight, R. C.: The potential of a circular cylinder between two infinite planes. Proc. London Math. Soc. 39, 272 (1933).

    Google Scholar 

  43. Labus, J.: Berechnung des elektrischen Feldes von Hochspannungstransformatoren mit Hilfe der konformen Abbildung. Arch. Elektrotechn. 19, 82 (1927).

    Article  Google Scholar 

  44. Labus, J.: Der Potential-und Feldverlauf längs einer Transformatorwicklung. Arch. Elektrotechn. 21, 250 (1928).

    Article  Google Scholar 

  45. Levi-Civita, T.: Sopra un problema di elettrostatica the si è presentato nella construzione dei cavi. Rend. Circ. Math. Palermo 20 (1905).

    Google Scholar 

  46. Levy, H.: Discontinuous fluid motion past a curved boundary. Proc. Roy. Soc. Lond. 92, 285 (1915).

    ADS  Google Scholar 

  47. Mclachlan, N. W.: Heat conduction in elliptical cylinder and an analogous electromagnetic problem. Phil. Mag. 36, 600 (1945).

    MathSciNet  MATH  Google Scholar 

  48. Meyer, E.: Zwei Beispiele zweidimensionaler elektrostatischer Kraftlinienbilder. Math. Ann. 93, 157 (1925).

    Article  MathSciNet  Google Scholar 

  49. Morton, W. B.: The electrification of two intersecting planes. Phil. Mag. 1, 337 (1926).

    MATH  Google Scholar 

  50. Morton, W. B.: On the parallel-plate condenser and other two-dimensional fields specified by elliptic functions. Phil. Mag. 2, 827 (1926).

    MATH  Google Scholar 

  51. Nicholson, J. W.: The electrification of two parallel circular disks. Phil. Trans. Roy. Soc. Lond. 224, 303 (1923/24).

    Google Scholar 

  52. Page, W. M.: Some two-dimensional problems in electrostatics and hydrodynamics. Proc. London Math. Soc. 11, 313 (1913).

    Google Scholar 

  53. Petersohn, H.: Zweidimensionale elektrostatische Probleme. Z. Physik 38, 727 (1926).

    Article  ADS  MATH  Google Scholar 

  54. Poole, E. G. C.: On the discontinuous motion produced in an infinite stream by two plane obstacles. Proc. London Math. Soc. 22, 425 (1924).

    MATH  Google Scholar 

  55. Poritsky, H.: Field due to two equally charged parallel conducting cylinders. J. Math. Phys. 11, 213 (1932).

    Google Scholar 

  56. Richmond, H. W.: On the electrostatic field of a plane or circular grating formed of thick rounded bars. Proc. London Math. Soc. 22, 389 (1924).

    MATH  Google Scholar 

  57. Richmond, H. W.: Notes on the use of the Schwartz-Christoffel transformation in electrostatics (and hydrodynamics). Proc. London Math. Soc. 22, 483 (1924).

    Google Scholar 

  58. Rogowski, W.: Die elektrische Festigkeit am Rande des Plattenkondensators. Arch. Elektrotechn. 12, 1 (1923).

    Article  Google Scholar 

  59. Siebeck, F. H.: Über eine Gattung von curven vierten Grades, welche mit den elliptischen Funktionen zusammenhängen. J. reine angew. Math. 57, 359 (1860).

    Article  MATH  Google Scholar 

  60. Thomson, J. J.: Recent researches in electricity and magnetism, Chap. 3. London: Oxford Univ. Press 1893.

    Google Scholar 

  61. Weber, E.: Die konforme Abbildung in der elektrischen Festigkeitslehre. Arch. Elektrotechn. 17, 174 (1926).

    Article  Google Scholar 

  62. Wright, C. E.: Note on the potential and attraction of rectangular bodies. Phil. Mag. 10, 110 (1930).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Massachusetts Institute of Technology, Cambridge, Mass., USA

    Parry Moon

  2. University of Connecticut, Storrs, Conn., USA

    Domina Eberle Spencer

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  1. Parry Moon
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  2. Domina Eberle Spencer
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© 1961 Springer-Verlag OHG / Berlin · Göttingen · Heidelberg

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Moon, P., Spencer, D.E. (1961). Cylindrical Systems. In: Field Theory Handbook. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-53060-9_3

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  • DOI: https://doi.org/10.1007/978-3-642-53060-9_3

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