By Gérard A. Maugin

Conceived as a sequence of roughly self reliant essays, the current publication 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 international battle, 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 relations, Euler, d’Alembert, Lagrange, Cauchy, Piola, Duhamel, Neumann, Clebsch, Kirchhoff, Helmholtz, Saint-Venant, Boussinesq, the Cosserat brothers, Caratheodory) in pageant 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 medical rules. The ebook indicates how the ambitious advancements that blossomed within the 20th century (and perused in a prior e-book of the writer within the similar Springer sequence: “Continuum Mechanics in the course of the 20th Century”, Springer 2013) stumbled on wealthy compost within the confident foundational achievements of the eighteenth and 19th centuries. The pre-WWI scenario is easily summarized by means of an intensive research of treatises (Appell, Hellinger) released at the moment. English translations through the writer of most crucial 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)

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Cambridge University Press, New York 3. Antman SS (1995) Nonlinear problems in elasticity. Springer, New York 4. Bernhard H (1983) The Bernoulli family. In: Wussing H, Arnold W (eds) Biographien bedeutender Mathematiker, Berlin 5. Bernoulli J (John) (1727) Theoremata selecta pro conservatione virium vivarum demonstranda et experimenta confirmanda. Comment Acad Scientarium Imperialis Petropolitanae 2:200–207 6. Bernoulli J (John) (1735) De vera notione virium vivarum earimque usu in dynamicis, ostenso per exemplum, propositumi.

This is in what the principle called the composition of forces consists. This principle suffices by itself to determine the laws of equilibrium in all cases; because, by composing all forces two by two, we must arrive at a unique force that is equivalent to all forces, and this, consequently, must vanish in the case of equilibrium, if there is no fixed point in the system. But if there is such a point, the direction of this unique force must go through this fixed point. , pulleys] is deduced uniquely from the principle we just spoke about.

Darboux, vol 2, pp 477–521, Gauthier-Villars, Paris) 28. Jouguet E (1924) Lectures de mécanique: La mécanique enseignée par les auteurs originaux. Gauthier-Villars, Paris (Facsimile reprint, Gabay, Paris, 2007) 29. Lagrange JL (1762) Essai d’une nouvelle méthode pour déterminer les maxima et les formules des intégrales minimum indéfinies. In: Serret JA, Darboux G (eds) Œuvres de Lagrange (1867–1892), vol 1, pp 335–362, Gauthier-Villars, Paris 30. Lagrange JL (1762) Application de la méthode exposée dans le mémoire précédent à la solution des problèmes de dynamique différents.

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