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Bulletin of the American Mathematical Society

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The influence of elasticity on analysis: The classic heritage

Author: C. Truesdell
Journal: Bull. Amer. Math. Soc. 9 (1983), 293-310
MSC (1980): Primary 73-02; Secondary 15-02, 53-02, 33-02, 33A25, 49-02
MathSciNet review: 714991
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  • A.-J.-C.-Barré de St. Venant, Historique abrégé des recherches sur la résistance et sur l'élasticité des corps solides, pp. xc-cccxj of C.-L.-M.-H. Navier, Resumé des Leçons...sur l'Application de la Mécanique..., Paris, Dunod, 1864.
  • I. Todhunder, A history of the theory of elasticity... (edited and completed by K. Pearson), Cambridge Univ. Press, Vol. 1, 1886, Vol. 2, 1893. Both of these histories are far from complete. For details of §§1-4:
  • C. Truesdell, The rational mechanics of flexible or elastic bodies, 1638–1788, Leonhardi Euleri Opera Omnia, Series secunda (Opera mechanica et astronoca), Vol. XI, sectio secunda. Auctoritate et impensis Societatis Scientiarum Nturalium Helveticae, Orell Fssli, Zürich, 1960. MR 0131341
  • C. Truesdell, Sophie Germain, Arch. Hist. Exact Sci. (in preparation).
  • C. Truesdell and R. Toupin, The classical field theories, Handbuch der Physik, Bd. III/1, Springer, Berlin, 1960, pp. 226–793; appendix, pp. 794–858. With an appendix on tensor fields by J. L. Ericksen. MR 0118005
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  • C. Truesdell and W. Noll, The nonlinear field theories of mechanics, op.cit., Vol. III/3, 1965.
  • C. Truesdell, Essays in the history of mechanics, Springer-Verlag New York Inc., New York, 1968. MR 0242616
  • M. E. Gurtin, The linear theory of elasticity, Encyclopedia of Physics (C. Truesdell, ed.), Vol. VIa/2, Springer-Verlag, Berlin, 1972, pp. 1-295.
  • J. E. Marsden and T. J. R. Hughes, Mathematical foundations of elasticity, Prentice-Hall, Englewood Cliffs, N.J., 1983.
  • C. C. Wang and C. Truesdell, Introduction to rational elasticity, Noordhoff International Publishing, Leyden, 1973. Monographs and Textbooks on Mechanics of Solids and Fluids: Mechanics of Continua. MR 0468442
  • C. Truesdell and R. G. Muncaster, Fundamentals of Maxwell’s kinetic theory of a simple monatomic gas, Pure and Applied Mathematics, vol. 83, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1980. Treated as a branch of rational mechanics. MR 554086
  • R. G. Muncaster, Invariant manifolds in mechanics: The general construction of coarse theories from fine theories, Arch. Rational Mech. Anal. (to appear).

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