Advertisement

A Course of Continuum Mechanics at the Dawn of the Twentieth Century (Volume III of Appell’s Treatise on Rational Mechanics)

  • Gérard A. MauginEmail author
Chapter
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 214)

Abstract

The treatise on rational mechanics published in French by Paul Appell starting in 1900 is a unique monument in the mathematical literature of the Pre-World War One period. Here we critically peruse the volume devoted to continuum mechanics (Volume III). This critical examination is performed in the light of what was known at the time, what were the fashionable themes in continuum mechanics in the early twentieth century, what mathematical techniques were preferred, and what was the naturally influential environment (especially among French mathematicians). All these gave a special tune and contents to a treatise that bears the print of its time, especially with an emphasis on subject matters such as potential theory, the consideration of complex variables, the interest for vortices, barotropic and “barocline” fluids, and new notions such as those put forward by J. Hadamard in wave propagation, by H. Villat and V. Bjerknes in fluid mechanics, and the many references to contemporary works by J.V. Boussinesq, A. Barré de Saint-Venant, H. Poincaré, P. Duhem, and the Cosserat brothers. In contrast, we note the few references to foreign works, the non-exploitation of the then recently proposed vectorial and tensorial concepts, and the lack of interest in dissipative behaviours, whether in fluids or in solids, this in accord with the bannered “rationality” of the treatise.

Keywords

Rational mechanics Continuum mechanics Lectures 

References

  1. 1.
    Anderson JD Jr (1997) A history of aerodynamics. Cambridge University Press, UKGoogle Scholar
  2. 2.
    Appell P (1921) Traité de mécanique rationnelle, 3rd edn. Gauthier-Villars, Paris (facsimilé reprint by Gabay, Paris, 1991)Google Scholar
  3. 3.
    Appell P (1925) Notice sur les travaux scientifiques. Acta Mathematica 45:161–285CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Appell P (1955) Traité de mécanique rationnelle, Tome V: «Eléments de calcul tensoriel: applications géométriques et mécaniques» by René Thiry. Gauthier-Villars, Paris; first edition 1926, second edition 1933; new printing 1955. (Editions Gabay, Paris, made the good move to reprint this together with the second edition (1935) of Volume IV in a facsimile reprint in 1991)Google Scholar
  5. 5.
    Basset AB (1890) An elementary treatise on hydrodynamics and sound. Deighton, Bell and Co., CambridgezbMATHGoogle Scholar
  6. 6.
    Bjerknes V, Bjerknes J, Solberg H, Bergeron T (1934) Hydrodynamique physique (avec applications à la météorologie dynamique), 3 volumes. Presses Universitaires de France, ParisGoogle Scholar
  7. 7.
    Bouguer P (1746) Traité du navire, de sa construction et de ses mouvements. Chez Jombert, Quai des Augustins, ParisGoogle Scholar
  8. 8.
    Brillouin M (1884–1885) Leçons sur l’élasticité et l’acoustique. Librairie Labouche, ToulouseGoogle Scholar
  9. 9.
    Brillouin L (1938) Les tenseurs en mécanique et élasticité. Masson, Paris (Dover reprint, New York, 1946; Gabay reprint, Paris, 2012; English Trans. Academic Press, New York, 1963)Google Scholar
  10. 10.
    Cauchy AL (1828) Sur les équations qui expriment l’équilibre ou les lois du mouvement intérieur d’un corps solide élastique ou non élastique. Exercices de mathématiques, vol 3. pp 160–187. (This presents in print the ideas originally submitted to the Paris Academy of Sciences on September 30, 1822)Google Scholar
  11. 11.
    Cauchy AL (1828) In: Exercices de Mathématiques, vol. 3. Pp 188–212. («De la pression ou tension dans un système de points matériels» Oct. 1828, pp 213–236)Google Scholar
  12. 12.
    Coffin JG (1914) Calcul vectoriel. Gauthier-Villars, Paris. (French translation by M. Véronnet of the English original “Vector calculus: An introduction to vector methods and their various applications to physics and mathematics”, 1909)Google Scholar
  13. 13.
    Cosserat E, Cosserat F (1896) Sur la théorie de l’élasticité. Ann Fac Sci Toulouse, 1ère série 10(3–5):I.1–I.116Google Scholar
  14. 14.
    Cosserat E, Cosserat F (1909) Théorie des corps déformables. Hermann, Paris, (226 pages). Reprint by Editions Gabay, Paris, 2008; Reprint by Hermann Archives, Paris, 2009, (English translation: N68-15456: Clearinghouse Federal Scientific and Technical Information, Springfield, Virginia NASA, TT F-11561 (February 1968); another translation by D. Delphenich, 2007) (originally published as supplement in pp 953–1173 to: Chwolson OD (1909), Traité de physique (traduit du Russe), vol II, Paris, Hermann)Google Scholar
  15. 15.
    Crowe MJ (1967) A history of vector analysis: The evolution of the idea of a vectorial system. University of Notre Dame Press (Dover reprint, New York, 1985)Google Scholar
  16. 16.
    de Saint-Venant BAJC (1883) Théorie des corps élastiques. (French translation from the German with many comments and additions of: Clebsch A (1862) Theorie der Elastizität fester Körper, Leipzig)Google Scholar
  17. 17.
    Duhem P (1891) Hydrodynamique, élasticité, acoustique. A. Hermann Editeur, ParisGoogle Scholar
  18. 18.
    Guyou E (1887). Théorie du navire. Berger-Levrault, Paris (Second edition, 1894)Google Scholar
  19. 19.
    Hadamard J (1903) Leçons sur la propagation des ondes et les équations de l’hydrodynamique. Hermann, PariszbMATHGoogle Scholar
  20. 20.
    Korteweg DJ, de Vries G (1895) On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves. Philos Mag 39(Series 3):422–443CrossRefzbMATHGoogle Scholar
  21. 21.
    Lamé G (1852) Leçons sur la théorie mathématique de l’élasticité des corps solides. Paris, (2nd edition, 1866) (Facsimile reprint, Gabay, Paris, 2006)Google Scholar
  22. 22.
    Lévy M (1890) L’hydrodynamique moderne et l’hypothèse des actions à distance. Revue Générale des Sciences Pures et Appliquées, December 15, 1890Google Scholar
  23. 23.
    Lichnerowicz A (1964) Eléments de calcul tensoriel, 7th edn. Armand Colin, Paris (Reprint by Gabay, Paris, 2011) (English translation by J.W. Leech, “Elements of Tensor Calculus. J. Wiley & Sons, New York, and Methuen & Co Ltd, UK, 1962)Google Scholar
  24. 24.
    Maugin GA (1976) Conditions de compatibilité pour une hypersurface singulière en mécanique relativiste des milieux continus. Ann Inst Henri Poincaré A24:213–241MathSciNetGoogle Scholar
  25. 25.
    Maugin GA (1992) The thermomechanics of plasticiy and fracture. Cambridge University Press, UKCrossRefGoogle Scholar
  26. 26.
    Maugin GA (2013) Continuum mechanics through the twentieth century: a concise historical perspective. Springer, DordrechtGoogle Scholar
  27. 27.
    Maugin GA (2013) About the Cosserats’ book of 1909 (preprint UPMC; see also Chapter 8 in the present book)Google Scholar
  28. 28.
    Poincaré H (1892) Leçons sur la théorie de l’élasticité. Georges Carré, Paris (Facsimile reprint, Gabay, 1990; also University of Michigan, Ann Arbor, 2012)Google Scholar
  29. 29.
    Poincaré H (1893) Théorie des tourbillons. Georges Carré, Paris (Facsimile reprint, Gabay, Paris, 1990)Google Scholar
  30. 30.
    Poincaré H (1899) Théorie du potentiel newtonien. Carré et Naud, Paris (Fasimile reprint, Gabay, Paris, 1990)Google Scholar
  31. 31.
    Prandtl L (1904) Ueber Flussigkeitsbewegung bei sehr kleiner Reibung. In: Contribution to the third international mathematical congress, HeidelbergGoogle Scholar
  32. 32.
    Riquier C (1905) Sur l’intégration d’un système d’équations aux dérivées partielles auquel conduit l’étude des déformations finies d’un milieu continu. Ann Ecole Norm Sup, Third series XXII: 475–538Google Scholar
  33. 33.
    Truesdell CA, Noll W (1965) The non-linear field theories of mechanics. In: Flügge S (ed) Handbuch der Physik, vol III/3. Springer, Berlin, pp 1–602Google Scholar
  34. 34.
    Truesdell CA, Toupin RA (1960) The classical theory of fields. In: Flügge S (ed) Handbuch der Physik, vol III/1. Springer, Berlin, pp 226–858Google Scholar
  35. 35.
    Villat H (1938) Mécanique des fluides, 2nd edn. Gauthier, Paris (First Edition, 1930; Facsimile reprint, Gabay, Paris, 2003)zbMATHGoogle Scholar
  36. 36.
    Wilson EB (1913) An advance in theoretical mechanics. Cosserat Bull Am Math Soc 19(5):242–246 (Théorie des corps déformables by E and F)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Institut Jean Le Rond d’AlembertUniversité Pierre et Marie CurieParis Cedex 05France

Personalised recommendations