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

By Gérard A. Maugin

Conceived as a chain of roughly independent essays, the current e-book seriously exposes the preliminary advancements of continuum thermo-mechanics in a publish Newtonian interval extending from the artistic works of the Bernoullis to the 1st international 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 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 historical past of medical rules. The publication indicates how the bold advancements that blossomed within the 20th century (and perused in a prior booklet of the writer within the related Springer sequence: “Continuum Mechanics throughout the 20th Century”, Springer 2013) came across wealthy compost within the optimistic foundational achievements of the eighteenth and 19th centuries. The pre-WWI scenario is easily summarized by way of a radical 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 advantage of the readers.

Show description

Read or Download Continuum Mechanics Through the Eighteenth and Nineteenth Centuries: Historical Perspectives from John Bernoulli (1727) to Ernst Hellinger (1914) PDF

Best mechanics books

MacLaurin's Physical Dissertations

The Scottish mathematician Colin MacLaurin (1698-1746) is better recognized for constructing and lengthening Newton's paintings in calculus, geometry and gravitation; his 2-volume paintings "Treatise of Fluxions" (1742) used to be the 1st systematic exposition of Newton's tools. it truly is renowned that MacLaurin was once offered prizes by way of the Royal Academy of Sciences, Paris, for his previous paintings at the collision of our bodies (1724) and the tides (1740); besides the fact that, the contents of those essays are much less commonly used - even though a number of the fabric is mentioned within the Treatise of Fluxions - and the essays themselves usually demanding to acquire.

DIANA Computational Mechanics ‘94: Proceedings of the First International Diana Conference on Computational Mechanics

Advances in computational mechanics can in basic terms be accomplished at the foundation of fruitful dialogue among researchers and practicing engineers. This has been accomplished within the current book, which includes the entire papers provided on the first foreign DIANA convention on Computational Mechanics.

Boundary Element Analysis in Computational Fracture Mechanics

The Boundary fundamental Equation (BIE) process has occupied me to numerous levels for the earlier twenty-two years. The appeal of BIE research has been its distinctive mix of arithmetic and sensible software. The EIE strategy is unforgiving in its requirement for mathe­ matical care and its requirement for diligence in developing powerful numerical algorithms.

Fracture Mechanics - Integration of Mechanics, Materials Science, and Chemistry

Fracture and "slow" crack development replicate the reaction of a cloth (i. e. , its microstructure) to the conjoint activities of mechanical and chemical using forces and are suffering from temperature. there's consequently a necessity for quantitative realizing and modeling of the impacts of chemical and thermal environments and of microstructure, when it comes to the major inner and exterior variables, and for his or her incorporation into layout and probabilistic implications.

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

Sample text

1) is replaced by a linear relationship (a linear vector relation in the language of Gibbs 3 The reader will be interested in Truesdell’s vision of Cauchy’s elaboration of the concept of stress in his Essay ‘‘The creation and unfolding of the concept of stress’’ in pp. 184–238 in Truesdell [45] (this was underlined by J. Casey, private communication). However, in contrast to the present study that emphasizes the story of the concept of stress from and after Cauchy, Truesdell deals with the conceptual stages that led to Cauchy’s notion of stress, with works by brilliant predecessors such as Stevins, Galileo Galilei, the Bernoullis, d’Alembert, Euler, Young, and Fresnel.

132]) and using no argument of geometry. He is even proud of the fact that no figures illustrate his exposition (although a few illustrations may have been welcomed). Lagrange in fact introduced a privileged tool for the ‘‘algebraïzation’’ of Mechanics. The second important point is that Lagrange, after some previous works by Clairaut [13] and Maupertuis [37] but above all with his introduction of generalized coordinates, really inaugurates an era where the recognition of invariance in mathematical physics has become fundamental.

In what follows I shall call motion of a body [here he means a point] the velocity of this same body considered on account of its direction, and call quantity of motion, in the ordinary sense, the product of mass by velocity. General problem. — Let a system of bodies be disposed in any manner with respect to one another, and let us suppose that we impose to each of these bodies a particular motion that it cannot follow because of the action exerted by other bodies: find out the motion that each body will take.

Download PDF sample

Rated 4.20 of 5 – based on 29 votes