Continuum Mechanics Through the Eighteenth and Nineteenth by Gérard A. Maugin

By Gérard A. Maugin

Conceived as a sequence of kind of self sustaining essays, the current e-book significantly exposes the preliminary advancements of continuum thermo-mechanics in a submit Newtonian interval extending from the inventive works of the Bernoullis to the 1st global conflict, 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 relatives, 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 heritage of medical rules. The ebook exhibits how the bold advancements that blossomed within the 20th century (and perused in a prior ebook of the writer within the comparable Springer sequence: “Continuum Mechanics in the course of the 20th Century”, Springer 2013) chanced on wealthy compost within the positive foundational achievements of the eighteenth and 19th centuries. The pre-WWI scenario is definitely summarized by means of a radical research of treatises (Appell, Hellinger) released at the moment. English translations via the writer of most important texts in French or German are given to the good thing about the readers.

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Extra info for Continuum Mechanics Through the Eighteenth and Nineteenth Centuries: Historical Perspectives from John Bernoulli (1727) to Ernst Hellinger (1914)

Example text

Thus, x ¼ "xða; b; c; tÞ; etc: He thus write the continuity equation as (in modern notation) dm ¼ q dx dy dz ¼ const: or q0 ¼ qJ: He introduces a scalar ‘‘Lagrange’’ multiplier to account for incompressibility. He obtains thus the three equations of balance of linear momentum equations in the ‘‘Lagrangian’’ format. But he also shows how to revert to an Eulerian description (Equation F in p. 264). He is quite honest in admitting that it may be easier to deal with Euler’s format (p. 265). , in a flute or an organ pipe).

The system would have remained at rest; it is clear that a, b, c, &c are the motions that the bodies will take by virtue of their action. Q. E. D. -L. Lagrange (1788), Méchanique analitique, 1st Edition, Veuve Desaint, Paris (1788) [after the reprint of the second revised edition of 1811/1815 with new title ‘‘Mécanique analytique’’ in two volumes, Veuve Courcier, Paris; reprinted by Gabay, Paris, 1997, from the fourth edition edited by J. Bertand and G. Darboux] by Gérard Maugin. Translator’s remarks are placed within square brackets in the main text.

Scientific thought is promoted together with a challenge of ideas that are too much grounded in tradition and faith. One of our heroes in this essay, d’Alembert, epitomizes the enlightened scientist who simultaneously wants to improve society and teach it through a pharaonic enterprise such as the production of the great ‘‘Encyclopédie’’ (ou Dictionnaire raisonné des sciences, des arts et des métiers) directed by him and Denis Diderot (1713–1784), and sold (by subscription) all over Europe in about 20,000 copies in spite of the bulk of thirty-five volumes.

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