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The Theory of the Top. Volume IV pp 761–936Cite as

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Technical applications

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Abstract

We cannot regret, in the interest of the subject matter, that this concluding volume of our work has appeared so late. Indeed, the principal technical applications that we consider here have arisen only in the last ten years, during the printing of this book; we recall the high-speed railway, the gyroscopic ship stabilizer, and the gyroscopic compass.

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References.

  1. Hermann Anschütz-Kämpfe, “Der Kreisel als Richtungsweiser auf der Erde mit besonderer Berücksichtigung seiner Verwendbarkeit auf Schiffen,” Jahrbuch der Schiffbautechnischen Gesellschaft, Vol. 10, 1909, pp. 352–369.

    Google Scholar 

  2. Fritz Bernhard Behr, “High-Speed Electrical Railways and the Proposed Monorail between Manchester and Liverpool,” Transactions of the Liverpool Engineering Society, Vol. XXIII, 1902, pp. 76–97; http://books.google.com.

  3. Wilhelm Behrens, “Ein der Theorie der Laval-Turbine entnommenes mechanisches Problem, behandelt mit Methoden der Himmelsmechanik,” Inaugural Dissertation, Georg-August-Üniversität in Göttingen, 1911, http://hathitrust.org; also Zeitschrift für Mathematik und Physik, Bd. 59, 1911, pp. 337–390.

  4. Franz Berger, “Zur Theorie des Schlickschen Schiffskreisels,” Zeitschrift des Vereines deutscher Ingenieure, Vol. 48, 1904, pp. 982–983.

    Google Scholar 

  5. Henry Bessemer, Sir Henry Bessemer, F. R. S., Offices of “Engineering,” London, 1905; http://books.google.com.

  6. Max Born, “Arnold Johannes Wilhelm Sommerfeld, 1868–1951,” Obituary Notices of Fellows of the Royal Society, Vol. 8, No. 21, 1958, pp. 274–296; http://jstor.org.

  7. Charles ´Emile Ernest Bourlet, Traitè des Bicycles et Bicyclettes, Gauthier-Villars, Paris, 1895; http://hathitrust.org.

  8. Gustav Brecht, “Schwerpunktslage u. Kreiselwirkungen bei elektrischen Lokomotiven,” Elektrische Kraftbetriebe u. Bahnen, Jahrgang VIII, 1910, pp. 121–127, 144–150, 161–167.

    Google Scholar 

  9. Louis Brennan, “Means for Imparting Stability to Unstable Bodies,” US Patent 796,893, 1905.

    Google Scholar 

  10. Jobst Broelmann, “The Development of the Gyrocompass— Inventors as Navigators,” Journal of Navigation, Vol. 51, No. 2, 1998, pp. 267–276.

    Article  Google Scholar 

  11. Jobst Broelmann, Intuition und Wissenschaft in der Kreiseltechnik, 1750 bis 1930, Deutsches Museum, Munich, 2002.

    Google Scholar 

  12. Robert Bud and Deborah Jean Warner, Instruments of Science: An Historical Perspective, Garland Publishing Co., New York, 1998.

    Google Scholar 

  13. The Whitehead Torpedo, Bureau of Ordnance, Department of the Navy, Naval Torpedo Station, Newport, R.I., 1998; http://www.hnsa.org.

  14. Emmanuel Carvallo, “Thèorie du mouvement du monocycle et de la bicyclette. Première partie. Cerceau et monocycle,” Journal de l’École Polytechnique, Sèr. II, Vol. 5, 1900, pp. 119–188; http://books.google.com.

  15. Emmanuel Carvallo, “Thèorie du mouvement du monocycle et de la bicyclette. Deuxième partie. Thèorie de la bicyclette,” Journal de l’École Polytechnique, Sèr. II, Vol. 6, 1901, pp. 1–118; http://books.google.com.

  16. Harold Crabtree, An Elementary Treatment of the Theory of Spinning Tops and Gyroscopic Motion, Longmans, Green and Co., London, 1909; http://books.google.com.

  17. Carl Cranz, Lehrbuch der Ballistik, B. G. Teubner, Leipzig, 1910; http://books.google.com.

  18. Carl Cranz, A translation of Cranz’s Textbook of ballistics, United States Office of Scientific Research and Development, Technical Reports Section for Armor and Ordnance, National Defense Committee, Washington, 1944.

    Google Scholar 

  19. Carl Dick and Otto Kretschmer, Handbuch der Seemannschaft, Part 2, Ernst Siegfried Mittler und Sohn, Berlin, 1902; http://books.google.com.

  20. Henry Winram Dickinson, A Short History of the Steam Engine, University Press, Cambridge, 1939.

    Google Scholar 

  21. Carl Diegel, “Selbstthätige Steuerung der Torpedos durch den Geradlaufapparat,” Marine-Rundschau, 10. Jahrgang, Heft 5, 1899, pp. 517–550; http://books.google.com.

  22. Edmond Dubois, Thèorie du Mouvement des Corps Cèlestes, Bertrand, Paris, 1864; http://gallica.bnf.fr.

  23. Edmond Dubois, “Sur le gyroscope marin,” Comptes Rendus, t. 98, 1884, pp. 227–229.

    Google Scholar 

  24. Michael Eckert, Arnold Sommerfeld: Science, Life and Turbulent Times, 1868–1951, English translation by Tom Artin, Springer, 2013.

    Google Scholar 

  25. Charles B. Edwards, “Builders’ Trials of Curtis Turbine Steamer ‘Creole,’ ” Engineering, Vol. 84, 1907, pp. 695–698; http://books.google.com.

  26. J. A. Faulkner, J. D. Clarke, and D. Faulkner, “The Loss of HMS COBRA—A Reassessment,” The Naval Architect, May 1985, pp. 125–151.

    Google Scholar 

  27. Georges Ernest Fleuriais, “Gyroscope-Collimateur, Substitution d’un Repère Artificiel a l’Horizon de la Mer,” Revue Maritime et Coloniale, Vol. 91, 1886, pp. 452–518; http://gallica.bnf.fr.

  28. August Föppl, “Das Problem der Laval’schen Turbinenwelle,” Der Civilingenieur, Bd. 16, 1895, pp. 333–342; http://hathitrust.org.

  29. August Föppl, “Die Theorie des Schlickschen Schiffskreisels,” Zeitschrift des Vereines deutscher Ingenieure, Vol. 48, 1904, pp. 487–483.

    Google Scholar 

  30. August Föppl, “Zuschriften an die Redaktion,” Zeitschrift des Vereines deutscher Ingenieure, Vol. 48, 1904, pp. 983–984.

    Google Scholar 

  31. August Föppl, Vorlesungen über technische Mechanik, Vol. VI, B. G. Teubner, Leipzig, 1910; http://books.google.com.

  32. Walther Gerlach and Arnold Sommerfeld, “Hermann Anschütz-Kaempfe,” Die Naturwissenschaften, Vol. 19, 1931, pp. 666–669.

    Google Scholar 

  33. George Greenhill, “Gyroscope and Gyrostat,” Encyclopædia Britannica, Vol. XII, University Press, Cambridge, 1911, pp. 769–779, http://books.google.com.

  34. Roger Huntington, “Are 4 wheels 2 too many?” Car and Driver, May 1961, pp. 43–45, 110–111.

    Google Scholar 

  35. Thomas Parke Hughes, Elmer Sperry, Inventor and Engineer, Johns Hopkins Press, Baltimore, 1971.

    Google Scholar 

  36. Rangs- und Eintheilungs-liste der k. u. k. Kriegsmarine, kaiserlich-königlichen Hof- und Staatsdruckerei, Wien, 1893; http://books.google.com.

  37. Felix Klein to Arnold Sommerfeld, 20 November 1907, Deutsches Museum Archive, HS 1977-28/A,170.

    Google Scholar 

  38. Felix Klein, Gesammelte Mathematische Abhandlungen, Band 2, edited by R. Fricke and H. Vermeil, Springer, 1922; http://archive.org.

  39. Ludwig Klein, “Theorie, Konstruktion und Nutzeffekt der Dampfturbinen,” Zeitschrift des Vereines deutscher Ingenieure, Bd. XXXIX, No. 40, 1895, pp. 754, 1189–1195.

    Google Scholar 

  40. Fritz Kötter, “Die Kreiselwirkung der Räderpaare bei regelmäsiger Bewegung des Wagens in kreisförmigen Bahnen,” Sitzungsberichte der Berliner Mathematischen Gesellschaft, Feb. 1904, pp. 36–45; appendix to Archiv der Mathematik und Physik, Bd. 7, 1904; http://books.google.com.

  41. J. D. G. Kooijman, J. P. Meijaard, J. M. Papadopolous, A. Ruina, and A. L. Schwab, “A bicycle can be made self-stable without gyroscopic or caster effects,” Science, Vol. 332, Issue 6027, 2011, pp. 339–342; http://www.sciencemagazine.org.

  42. Alexei Nikolaevich Krylov and Conrad Heinrich Müller, “Die Theorie des Schiffes,” Encyklopädie der mathematischen Wissenschaften, Band IV, Teil 3, Art. 22, B. G. Teubner, Leipzig, 1901–1908, pp. 517–593; http://gdz.sub.uni-goettingen.de.

  43. Wilhelm Kübler, “The Scherl Monorail-road of Germany,” The American Machinist, Vol. XXXII, Part 2, 1909, pp. 1135- 1138; http://books.google.com.

  44. Lev Davidovich Landau and Evgeny Mikhailovich Lifshitz, Mechanics, Pergamon Press, Oxford, 1960.

    Google Scholar 

  45. Oskar Lasche, “High-Speed Electrical Traction in Germany,” Engineering, Vol. 72, 1901, pp. 369–370, 558.

    Google Scholar 

  46. Dieter Lohmeier and Bernhardt Schell, Einstein, Ansch ütz und der Kieler Kreiselkompass, Raytheon Marine GmbH, Kiel, 2005.

    Google Scholar 

  47. Hans Lorenz, “Die Wirkung eines Kreisels auf die Rollbewegung von Schiffen,” Physikalische Zeitschrift, 5. Jahrgang, 1904, p. 27–32; http://books.google.com.

  48. Alfred Lucas, Des Phènomènes Gyroscopiques et de leurs Principales Applications à la Navigation, Vol. IV, Challamel, Paris, 1918; http://hathitrust.org.

  49. William Duncan MacMillan, Dynamics of Rigid Bodies, Dover Publications, New York, 1960.

    Google Scholar 

  50. Wilhelm Magnus and Fritz Oberhettinger, Formulas and Theorems for the Functions of Mathematical Physics, Chelsea Publishing Co., New York, 1954.

    Google Scholar 

  51. Rurik Malmström, “Versuch einer Theorie der elektrolytischen Dissoziation unter Berücksichtigung der elektrischen Energie,” Leipzig, 1905; http://books.google.com.

  52. Rurik Malmström, “Die Theorie des Schlick’schen Schiffskreisels,” Acta societatis scientiarum Fennicæ, Tom. XXXV, No. 2, 1909.

    Google Scholar 

  53. Oscar Martienssen, “Die Verwendbarkeit des Rotationskompasses als Ersatz des magnetischen Kompasses,” Physikalische Zeitschrift, Vol. 7, No. 15, 1906, pp. 535–543.

    MATH  Google Scholar 

  54. Oscar Martienssen, “Die Entwicklung des Kreiselkompasses,” Zeitschrift des Vereines deutscher Ingenieure, Vol. 67, No. 8, 1923, pp. 182–187.

    Google Scholar 

  55. James Clerk Maxwell, “Address to the Mathematical and Physical Sections of the British Association,” Nature, Vol. 2, No. 47, 1870, pp. 419–428; reprinted in The Scientific Papers of James Clerk Maxwell, Vol. II, Cambridge University Press, 1890, pp. 215–229; http://books.google.com.

  56. J. P. Meijaard, J. M. Papadopolous, A. Ruina, and A. L. Schwab, “Linearized dynamics equations for the balance and steer of a bicycle: a benchmark and review,” Proceedings of the Royal Society A, Vol. 463, 2007, pp. 1955–1982; http://rspa.royalsocietypublishing.org.

  57. Heinrich Meldau, “Nautik,” Encyklopädie der mathematischen Wissenschaften, Band VI, Teil 1, Art. 5, B. G. Teubner, Leipzig, 1906–1925, pp. 297–372; http://gdz.sub.uni-goettingen.de.

  58. Paul F. Mottelay, “The Regnard Aeroplane,” Scientific American Supplement, Vol. LXX, No. 1814, 1910, pp. 228–229; http://books.google.com.

  59. Gottfried Noether, “Fritz Noether (1884-194?),” Integral Equations and Operator Theory, Vol. 8, 1985, pp. 573–576.

    Article  MATH  MathSciNet  Google Scholar 

  60. Andrei Parastaev, “Letter to the Editor,” Integral Equations and Operator Theory, Vol. 13, 1990, pp. 303–305.

    Article  MathSciNet  Google Scholar 

  61. John Perry, Spinning Tops and Gyroscopic Motions, Dover Publications, New York, 1957.

    Google Scholar 

  62. Ludwig Prandtl, “Einige für die Flugtechnik wichtige Beziehungen aus der Mechanik,” Zeitschrift für Flugtechnik und Motorluftschiffahrt, Jahrgang 1, 1910, pp. 3–6, 25–30, 61–64, 74–76; http://hathitrust.org.

  63. William John Macquorn Rankine, “On the dynamical principles of the motion of velocipedes,” The Engineer, Vol. 28, 1869, pp. 79, 129, 153, 175, Vol. 29, 1870, p. 2; http://gracesguide.co.uk.

  64. Paul Louis Antoine Regnard, “Automatic Stabilizer for Aeroplanes and the Like,” US Patent 1,015,837, 1912; http://uspto.gov.

  65. Edward John Routh, The Elementary Part of a Treatise on the Dynamics of a System of Rigid Bodies, Dover Publications, New York, 1960.

    Google Scholar 

  66. Renato de Santis and Michele Russo, “Rolling of the S. S. ‘Conte di Savoia’ in Tank Experiments and at Sea,” Transactions of the Society of Naval Architects and Marine Engineers, Vol. 44, 1936, pp. 169–194.

    Google Scholar 

  67. August Scherl, Ein neues Schnellbahnsystem, Druck und Verlag von August Scherl, 1909; http://commons.wikimedia.org.

  68. Otto Schlick, “Der Schiffskreisel,” Jahrbuch der Schiffbautechnischen Gesellschaft, Bd. 10, 1909, pp. 111–148.

    Google Scholar 

  69. Karl-Heinz Schlote, “Fritz Noether – Opfer zweier Diktaturen. Tod und Rehabilitierung,” NTM Shriftenreihe für Geschichte der Naturwissenschaften und Medizin, Vol. 28, 1991, pp. 33–41.

    Google Scholar 

  70. Max Schuler, “Die Störung von Pendel- und Kreiselapparten durch Beschleunigung des Fahrzeuges,” Physikalische Zeitschrift, Vol. 24, 1923, pp. 344–350.

    MATH  Google Scholar 

  71. Walter J. Sears, “The Whitehead Torpedo,” Engineering, Vol. 66, 1998, pp. 89–91; http://books.google.com.

  72. Francesco Siacci, Balistica, F. Casanova, Torino, 1888; http://books.google.com.

  73. Robert H. Silliman, “William Thomson: Smoke Rings and Nineteenth-Century Atomism,” Isis, Vol. 54, No. 4, 1963, pp. 461–474; http://jstor.org.

  74. Arnold Sommerfeld to Felix Klein, 8 November 1904, in Arnold Sommerfeld. Wissenschaftlicher Briefwechsel, Band 1, 1892-1918, p. 238, edited by Michael Eckert and Karl Märker, GNT-Verlag and Deutsches Museum, 2000.

    Google Scholar 

  75. Arnold Sommerfeld, “Mechanische Darstellung der electromagnetischen Erscheinungen in ruhenden Köpern,” Annalen der Physik, Bd. 46, 1892, pp. 139–151; reprinted in Arnold Sommerfeld, Gesammelte Schriften, Bd. I, Friedr. Vieweg & Sohn, Braunschweig, 1968, pp. 404–416.

    Google Scholar 

  76. Arnold Sommerfeld to the Russian Academy, 6 August 1940, carbon copy in Deutsches Museum Archive, NL 89, 024.

    Google Scholar 

  77. Arnold Sommerfeld, Mechanics, Lectures on Theoretical Physics, Vol. I, translated from the fourth German edition by Martin O. Stern, Academic Press, 1952.

    Google Scholar 

  78. Paul Gustav Stäckel, “Elementare Dynamik der Punktsysteme und starren Körper,” Encyklopädie der mathematischen Wissenschaften, Band IV, Teil 1, Art. 6, B. G. Teubner, Leipzig, 1901–1908, pp. 435–684; http://gdz.sub.uni-goettingen.de.

  79. Aurel Stodola, Steam Turbines, English translation by Louis C. Loewenstein, D. Van Nostrand, New York, 1905; http://books.google.com.

  80. Joseph John Thomson, A Treatise on the Motion of Vortex Rings, Macmillan and Co., London, 1883; http://books.google.com.

  81. William Thomson, Mathematical and Physical Papers, Vol. III, C. J. Clay and Sons, London, 1890; http://archive.org. 1002

  82. William Thomson, Mathematical and Physical Papers, Vol. IV, University Press, Cambridge, 1910, pp. 475–481; http://books.google.com.

  83. Norman Tomlinson, Louis Brennan, Inventor Extraordinaire, John Hallewell Publications, 1980.

    Google Scholar 

  84. David Gordon Tucker, “F. B. Behr’s Development of the Lartigue Monorail: From Country Crawler to Electric Express,” Transactions of the Newcomen Society, Vol. 55, 1983–84, pp. 131–152.

    Google Scholar 

  85. Gilbert Thomas Walker, “Spiel und Sport,” Encyklop ädie der mathematischen Wissenschaften, Band IV, Teil 2, Art. 9, B. G. Teubner, Leipzig, 1904–1935, pp. 127–152, http://gdz.sub.unigoettingen.de.

  86. Wilhelm Wechmann, “Gustav Wittfeld †,” Zentralblatt der Bauverwaltung, 43. Jahrgang, Nr. 85/86, 1923, p. 515; http://kobv.de.

  87. FranzWelz (tr.), The Berlin-Zossen Electric Railway Tests of 1903, McGraw Publishing Co., New York, 1905; http://archive.org.

  88. Francis JohnWelsh Whipple, “The stability of the motion of a bicycle,” Quarterly Journal of Pure and Applied Mathematics, Vol. XXX, 1899, pp. 312–348; http://hruina.tam.cornell.edu.

  89. Edmund Taylor Whittaker, Analytical Dynamics of Particle and Rigid Bodies, Cambridge University Press, 1964; http://archive.org (1917 ed.).

  90. William Dwight Whitney The Century Dictionary, The Century Co., New York, Vol. III, 1889; http://archive.org.

  91. Arthur Mason Worthington, Dynamics of Rotation, Longmans, Green, and Co., London, 1920; http://books.google.com.

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Authors and Affiliations

  1. Universität Göttingen Mathematisches Institut, Göttingen, Germany

    Felix Klein

  2. Universität München Fak. Mathematik, München, Germany

    Arnold Sommerfeld

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  1. Felix Klein
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  2. Arnold Sommerfeld
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Klein, F., Sommerfeld, A. (2014). Technical applications. In: The Theory of the Top. Volume IV. Birkhäuser, New York, NY. https://doi.org/10.1007/978-0-8176-4829-9_1

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