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Technical applications

  • Felix Klein
  • Arnold Sommerfeld
Chapter

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.

Keywords

Free Oscillation Rolling Motion Front Wheel Rear Wheel Pitching Motion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References.

  1. [Anschütz-Kämpfe 1909].
    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. [Behr 1902].
    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. [Behrens 1911].
    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. [Berger 1904].
    Franz Berger, “Zur Theorie des Schlickschen Schiffskreisels,” Zeitschrift des Vereines deutscher Ingenieure, Vol. 48, 1904, pp. 982–983.Google Scholar
  5. [Bessemer 1905].
    Henry Bessemer, Sir Henry Bessemer, F. R. S., Offices of “Engineering,” London, 1905; http://books.google.com.
  6. [Born 1952].
    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. [Bourlet 1895].
    Charles ´Emile Ernest Bourlet, Traitè des Bicycles et Bicyclettes, Gauthier-Villars, Paris, 1895; http://hathitrust.org.
  8. [Brecht 1910].
    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. [Brennan 1905].
    Louis Brennan, “Means for Imparting Stability to Unstable Bodies,” US Patent 796,893, 1905.Google Scholar
  10. [Broelmann 1998].
    Jobst Broelmann, “The Development of the Gyrocompass— Inventors as Navigators,” Journal of Navigation, Vol. 51, No. 2, 1998, pp. 267–276.CrossRefGoogle Scholar
  11. [Broelmann 2002].
    Jobst Broelmann, Intuition und Wissenschaft in der Kreiseltechnik, 1750 bis 1930, Deutsches Museum, Munich, 2002.Google Scholar
  12. [Bud 1998].
    Robert Bud and Deborah Jean Warner, Instruments of Science: An Historical Perspective, Garland Publishing Co., New York, 1998.Google Scholar
  13. [Bureau of Ordnance 1898].
    The Whitehead Torpedo, Bureau of Ordnance, Department of the Navy, Naval Torpedo Station, Newport, R.I., 1998; http://www.hnsa.org.
  14. [Carvallo 1900].
    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. [Carvallo 1901].
    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. [Crabtree 1909].
    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. [Cranz 1910].
    Carl Cranz, Lehrbuch der Ballistik, B. G. Teubner, Leipzig, 1910; http://books.google.com.
  18. [Cranz 1944].
    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. [Dick 1902].
    Carl Dick and Otto Kretschmer, Handbuch der Seemannschaft, Part 2, Ernst Siegfried Mittler und Sohn, Berlin, 1902; http://books.google.com.
  20. [Dickinson 1939].
    Henry Winram Dickinson, A Short History of the Steam Engine, University Press, Cambridge, 1939.Google Scholar
  21. [Diegel 1899].
    Carl Diegel, “Selbstthätige Steuerung der Torpedos durch den Geradlaufapparat,” Marine-Rundschau, 10. Jahrgang, Heft 5, 1899, pp. 517–550; http://books.google.com.
  22. [Dubois 1864].
    Edmond Dubois, Thèorie du Mouvement des Corps Cèlestes, Bertrand, Paris, 1864; http://gallica.bnf.fr.
  23. [Dubois 1884].
    Edmond Dubois, “Sur le gyroscope marin,” Comptes Rendus, t. 98, 1884, pp. 227–229.Google Scholar
  24. [Eckert 2013].
    Michael Eckert, Arnold Sommerfeld: Science, Life and Turbulent Times, 1868–1951, English translation by Tom Artin, Springer, 2013.Google Scholar
  25. [Edwards 1907].
    Charles B. Edwards, “Builders’ Trials of Curtis Turbine Steamer ‘Creole,’ ” Engineering, Vol. 84, 1907, pp. 695–698; http://books.google.com.
  26. [Faulkner 1985].
    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. [Fleuriais 1886].
    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. [Föppl 1895].
    August Föppl, “Das Problem der Laval’schen Turbinenwelle,” Der Civilingenieur, Bd. 16, 1895, pp. 333–342; http://hathitrust.org.
  29. [Föppl 1904a].
    August Föppl, “Die Theorie des Schlickschen Schiffskreisels,” Zeitschrift des Vereines deutscher Ingenieure, Vol. 48, 1904, pp. 487–483.Google Scholar
  30. [Föppl 1904b].
    August Föppl, “Zuschriften an die Redaktion,” Zeitschrift des Vereines deutscher Ingenieure, Vol. 48, 1904, pp. 983–984.Google Scholar
  31. [Föppl 1910].
    August Föppl, Vorlesungen über technische Mechanik, Vol. VI, B. G. Teubner, Leipzig, 1910; http://books.google.com.
  32. [Gerlach 1931].
    Walther Gerlach and Arnold Sommerfeld, “Hermann Anschütz-Kaempfe,” Die Naturwissenschaften, Vol. 19, 1931, pp. 666–669.Google Scholar
  33. [Greenhill 1911].
    George Greenhill, “Gyroscope and Gyrostat,” Encyclopædia Britannica, Vol. XII, University Press, Cambridge, 1911, pp. 769–779, http://books.google.com.
  34. [Huntington 1961].
    Roger Huntington, “Are 4 wheels 2 too many?” Car and Driver, May 1961, pp. 43–45, 110–111.Google Scholar
  35. [Hughes 1971].
    Thomas Parke Hughes, Elmer Sperry, Inventor and Engineer, Johns Hopkins Press, Baltimore, 1971.Google Scholar
  36. [k. u. k. Kriegsmarine 1893].
    Rangs- und Eintheilungs-liste der k. u. k. Kriegsmarine, kaiserlich-königlichen Hof- und Staatsdruckerei, Wien, 1893; http://books.google.com.
  37. [Klein 1907].
    Felix Klein to Arnold Sommerfeld, 20 November 1907, Deutsches Museum Archive, HS 1977-28/A,170.Google Scholar
  38. [Klein 1922].
    Felix Klein, Gesammelte Mathematische Abhandlungen, Band 2, edited by R. Fricke and H. Vermeil, Springer, 1922; http://archive.org.
  39. [Klein 1895].
    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. [Kötter 1904].
    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. [Kooijman 2011].
    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. [Krylov 1901].
    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. [Kübler 1909].
    Wilhelm Kübler, “The Scherl Monorail-road of Germany,” The American Machinist, Vol. XXXII, Part 2, 1909, pp. 1135- 1138; http://books.google.com.
  44. [Landau 1960].
    Lev Davidovich Landau and Evgeny Mikhailovich Lifshitz, Mechanics, Pergamon Press, Oxford, 1960.Google Scholar
  45. [Lasche 1901].
    Oskar Lasche, “High-Speed Electrical Traction in Germany,” Engineering, Vol. 72, 1901, pp. 369–370, 558.Google Scholar
  46. [Lohmeier 2005].
    Dieter Lohmeier and Bernhardt Schell, Einstein, Ansch ütz und der Kieler Kreiselkompass, Raytheon Marine GmbH, Kiel, 2005.Google Scholar
  47. [Lorenz 1904].
    Hans Lorenz, “Die Wirkung eines Kreisels auf die Rollbewegung von Schiffen,” Physikalische Zeitschrift, 5. Jahrgang, 1904, p. 27–32; http://books.google.com.
  48. [Lucas 1918].
    Alfred Lucas, Des Phènomènes Gyroscopiques et de leurs Principales Applications à la Navigation, Vol. IV, Challamel, Paris, 1918; http://hathitrust.org.
  49. [MacMillan 1960].
    William Duncan MacMillan, Dynamics of Rigid Bodies, Dover Publications, New York, 1960.Google Scholar
  50. [Magnus 1954].
    Wilhelm Magnus and Fritz Oberhettinger, Formulas and Theorems for the Functions of Mathematical Physics, Chelsea Publishing Co., New York, 1954.Google Scholar
  51. [Malmström 1905].
    Rurik Malmström, “Versuch einer Theorie der elektrolytischen Dissoziation unter Berücksichtigung der elektrischen Energie,” Leipzig, 1905; http://books.google.com.
  52. [Malmström 1909].
    Rurik Malmström, “Die Theorie des Schlick’schen Schiffskreisels,” Acta societatis scientiarum Fennicæ, Tom. XXXV, No. 2, 1909.Google Scholar
  53. [Martienssen 1906].
    Oscar Martienssen, “Die Verwendbarkeit des Rotationskompasses als Ersatz des magnetischen Kompasses,” Physikalische Zeitschrift, Vol. 7, No. 15, 1906, pp. 535–543.MATHGoogle Scholar
  54. [Martienssen 1923].
    Oscar Martienssen, “Die Entwicklung des Kreiselkompasses,” Zeitschrift des Vereines deutscher Ingenieure, Vol. 67, No. 8, 1923, pp. 182–187.Google Scholar
  55. [Maxwell 1870].
    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. [Meijaard 2007].
    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. [Meldau 1906].
    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. [Mottelay 1910].
    Paul F. Mottelay, “The Regnard Aeroplane,” Scientific American Supplement, Vol. LXX, No. 1814, 1910, pp. 228–229; http://books.google.com.
  59. [Noether 1985].
    Gottfried Noether, “Fritz Noether (1884-194?),” Integral Equations and Operator Theory, Vol. 8, 1985, pp. 573–576.CrossRefMATHMathSciNetGoogle Scholar
  60. [Parastaev 1990].
    Andrei Parastaev, “Letter to the Editor,” Integral Equations and Operator Theory, Vol. 13, 1990, pp. 303–305.CrossRefMathSciNetGoogle Scholar
  61. [Perry 1957].
    John Perry, Spinning Tops and Gyroscopic Motions, Dover Publications, New York, 1957.Google Scholar
  62. [Prandtl 1910].
    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. [Rankine 1869].
    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. [Regnard 1912].
    Paul Louis Antoine Regnard, “Automatic Stabilizer for Aeroplanes and the Like,” US Patent 1,015,837, 1912; http://uspto.gov.
  65. [Routh 1960].
    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. [de Santis 1936].
    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. [Scherl 1909].
    August Scherl, Ein neues Schnellbahnsystem, Druck und Verlag von August Scherl, 1909; http://commons.wikimedia.org.
  68. [Schlick 1909].
    Otto Schlick, “Der Schiffskreisel,” Jahrbuch der Schiffbautechnischen Gesellschaft, Bd. 10, 1909, pp. 111–148.Google Scholar
  69. [Schlote 1991].
    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. [Schuler 1923].
    Max Schuler, “Die Störung von Pendel- und Kreiselapparten durch Beschleunigung des Fahrzeuges,” Physikalische Zeitschrift, Vol. 24, 1923, pp. 344–350.MATHGoogle Scholar
  71. [Sears 1898].
    Walter J. Sears, “The Whitehead Torpedo,” Engineering, Vol. 66, 1998, pp. 89–91; http://books.google.com.
  72. [Siacci 1888].
    Francesco Siacci, Balistica, F. Casanova, Torino, 1888; http://books.google.com.
  73. [Silliman 1963].
    Robert H. Silliman, “William Thomson: Smoke Rings and Nineteenth-Century Atomism,” Isis, Vol. 54, No. 4, 1963, pp. 461–474; http://jstor.org.
  74. [Sommerfeld 1904].
    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. [Sommerfeld 1892].
    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. [Sommerfeld 1940].
    Arnold Sommerfeld to the Russian Academy, 6 August 1940, carbon copy in Deutsches Museum Archive, NL 89, 024.Google Scholar
  77. [Sommerfeld 1952].
    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. [Stäckel 1901].
    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. [Stodola 1905].
    Aurel Stodola, Steam Turbines, English translation by Louis C. Loewenstein, D. Van Nostrand, New York, 1905; http://books.google.com.
  80. [Thomson 1883].
    Joseph John Thomson, A Treatise on the Motion of Vortex Rings, Macmillan and Co., London, 1883; http://books.google.com.
  81. [Thomson 1890].
    William Thomson, Mathematical and Physical Papers, Vol. III, C. J. Clay and Sons, London, 1890; http://archive.org. 1002
  82. [Thomson 1910].
    William Thomson, Mathematical and Physical Papers, Vol. IV, University Press, Cambridge, 1910, pp. 475–481; http://books.google.com.
  83. [Tomlinson 1980].
    Norman Tomlinson, Louis Brennan, Inventor Extraordinaire, John Hallewell Publications, 1980.Google Scholar
  84. [Tucker 1983–84].
    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. [Walker 1904].
    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. [Wechmann 1923].
    Wilhelm Wechmann, “Gustav Wittfeld †,” Zentralblatt der Bauverwaltung, 43. Jahrgang, Nr. 85/86, 1923, p. 515; http://kobv.de.
  87. [Welz 1905].
    FranzWelz (tr.), The Berlin-Zossen Electric Railway Tests of 1903, McGraw Publishing Co., New York, 1905; http://archive.org.
  88. [Whipple 1899].
    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. [Whittaker 1964].
    Edmund Taylor Whittaker, Analytical Dynamics of Particle and Rigid Bodies, Cambridge University Press, 1964; http://archive.org (1917 ed.).
  90. [Whitney 1889].
    William Dwight Whitney The Century Dictionary, The Century Co., New York, Vol. III, 1889; http://archive.org.
  91. [Worthington 1920].
    Arthur Mason Worthington, Dynamics of Rotation, Longmans, Green, and Co., London, 1920; http://books.google.com.

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Felix Klein
    • 1
  • Arnold Sommerfeld
    • 2
  1. 1.Universität Göttingen Mathematisches InstitutGöttingenGermany
  2. 2.Universität München Fak. MathematikMünchenGermany

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