Continuum Mechanics Through the Eighteenth and Nineteenth - download pdf or read online

By Gérard A. Maugin

ISBN-10: 3319053736

ISBN-13: 9783319053738

ISBN-10: 3319053744

ISBN-13: 9783319053745

Conceived as a sequence of roughly self sustaining essays, the current e-book severely exposes the preliminary advancements of continuum thermo-mechanics in a put up Newtonian interval extending from the inventive works of the Bernoullis to the 1st global struggle, i.e., approximately in the course of first the “Age of cause” and subsequent the “Birth of the fashionable world”. The emphasis is rightly put on the unique contributions from the “Continental” scientists (the Bernoulli kinfolk, Euler, d’Alembert, Lagrange, Cauchy, Piola, Duhamel, Neumann, Clebsch, Kirchhoff, Helmholtz, Saint-Venant, Boussinesq, the Cosserat brothers, Caratheodory) in festival with their British friends (Green, Kelvin, Stokes, Maxwell, Rayleigh, Love,..). It underlines the most breakthroughs in addition to the secondary ones. It highlights the position of scientists who left crucial prints during this background of clinical principles. The publication exhibits how the bold advancements that blossomed within the 20th century (and perused in a prior publication of the writer within the related Springer sequence: “Continuum Mechanics during the 20th Century”, Springer 2013) stumbled on wealthy compost within the positive foundational achievements of the eighteenth and 19th centuries. The pre-WWI scenario is easily summarized through a radical research of treatises (Appell, Hellinger) released at the moment. English translations by way of the writer of most crucial texts in French or German are given to the advantage of the readers.

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78, Footnote 2, of Duhem [14]). The original record of this session is reproduced at the end of this chapter. It simply says that Cauchy read about his research (probably just the basic ideas) that was to be printed as a long abstract four months later in the Bulletin of the Société Philomatique. 2 Preliminary Remarks 35 is translated into English in the Appendix]. H. Navier (1785–1836)—another great elastician and fluid dynamicist—that delayed the real publication (see [1, pp. 97–98]). All his life Cauchy, an already mentioned prolific author, flooded the Académie with notes and memoirs, so much that the Académie at a point decided to fix an upper limit to the number of such contributions that any member could submit!

The discussion introduces other secondary stress definitions such as those by Piola, Kirchhoff, and more recently Eshelby. , in Cosserat continua), and whether some introduced stresses have associated with them a meaningful boundary condition. Also pondered is the question whether one can identify a stress concept in physical approaches still considering interactions between point particles (lattice dynamics, kinetic theory, nonlocal theory, statistical-mechanics approach). The chapter is concluded by a more in depth discussion of the notion of stress-energy-momentum, culminating in that of pseudo-tensor of energy-momentum in gravitation theory.

92], may have ‘‘provided the inspiration for further research in mathematical physics’’, in particular the mechanics of continua, although he had already taught some mechanics at the Ecole Polytechnique and at the Collège de France. The second fact which may a priori seem irrelevant to a scientific discussion, is the marriage of Cauchy with a certain Miss Aloïse de Bure in 1818. This, as we shall see, had a definite consequence on the manner of publishing his works by Cauchy. Now, the title of the present chapter does not question what happened all over the whole world, but more precisely what happened on that precise day of 1822 at the Academy of Sciences in Paris.

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Continuum Mechanics Through the Eighteenth and Nineteenth Centuries: Historical Perspectives from John Bernoulli (1727) to Ernst Hellinger (1914) by Gérard A. Maugin


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