By Gérard A. Maugin

Conceived as a sequence of kind of independent essays, the current ebook severely exposes the preliminary advancements of continuum thermo-mechanics in a put up Newtonian interval extending from the artistic 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 family members, 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 function of scientists who left crucial prints during this background of medical principles. The publication 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 optimistic foundational achievements of the eighteenth and 19th centuries. The pre-WWI scenario is easily summarized via 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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**Extra resources for Continuum Mechanics Through the Eighteenth and Nineteenth Centuries: Historical Perspectives from John Bernoulli (1727) to Ernst Hellinger (1914)**

**Example text**

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. Comment Petropolit Acta Eruditorum, Lipsiae (Leipzig), p 21 7. Bernoulli J (John) (1739) Hydraulica, nunc primum detecta ac demonstrata ex fundamentis pure mechanicis.

It is symptomatic that we technically concluded the present essay with the publication of Lagrange’s ‘‘Analytic Mechanics’’ in 1788, just one year before the French revolution (perhaps not always the best realization of the Enlightenment). 7 The Age of Reason: Conclusion and Things to Come • • • • • • 21 the fundamental equations of hydrodynamics [25] the principle of linear momentum [24] the equations of motion of rigid bodies (Euler) the principle of moment of momentum [24] the calculus of variations (John Bernoulli [6], Euler [23], Lagrange [29, 30]) analytic mechanics [31].

What is the primary quantity appearing in these equations? For engineers avoiding a dynamical framework—Eq. 2). 6) as a nonstrict conservation law for linear momentum prevails, the notion of associated flux being only secondary. 3) as Fext þ Fint þ Fa ¼ 0; ð3:13Þ Fext ¼ qf; Fint ¼ divr; Fa ¼ Àqa; ð3:14Þ where are volume forces of external, internal, and acceleration origin, respectively. 14) and the notion of Cauchy stress. This ‘‘definition’’ indicates that Fint is defined up to a divergence-free second-order tensor.