The Land Clearers and the “Classics”

Abstract

This chapter has for object to remind the reader of the early developments of continuum mechanics-after the seminal works in mechanics by Descartes, Huygens, Newton and Leibniz-in the expert hands of the initiators of this science (the Bernoulli family, d’Alembert, Euler, Lagrange). This was rapidly followed by the foundational contributions of the first half of the Nineteenth century with Cauchy and Navier (in France), Piola (in Italy), Kirchhoff (in Germany), and those of various giants of science such as Green, Kelvin, Stokes, Maxwell, Boussinesq, Poiseuille, Clebsch, von Helmholtz, Voigt, Mohr, and Barré de Saint-Venant later in the century. The emphasis is placed on the role played by so-called “ingénieurs-savants”, many of them educated at the French Ecole Polytechnique and the engineering schools inspired by this school all over Europe. Lamé, Navier and Duhamel in France and their Italian colleagues are examples of such people who harmoniously combined works in a much wanted contribution to civil engineering and a sure mathematical expertise in analysis. In contrast, the German and English contributors were more inclined towards an emerging true mechanical engineering and sometimes a burgeoning mathematical physics. This means that various national styles were being created despite the overall solution power of analysis and the birth of linear and tensor algebras.

In general a direct intrinsic notation is used for vectors and tensors, but a Cartesian index notation is introduced when a risk of confusion arises with the intrinsic one.