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The Dialectic Relation Between Physics and Mathematics in the XIXth CenturyMathematical Physics in Italy in the XIX Century: The Theory of Elasticity

The Dialectic Relation Between Physics and Mathematics in the XIXth Century: Mathematical Physics... [In the second half of the nineteenth century there was in Italy an important group of mathematicians who focused their attention on mathematical physics. The most prominent of them were Enrico Betti, Eugenio Beltrami, Gregorio Ricci–Curbastro and some others (Vito Volterra, Carlo Somigliana and Tullio Levi Civita) whose activity persevered for many years in the twentieth century. In this article, I will write about the contribution of this group to the theory of elasticity. The best representative writing on continuum mechanics and elasticity as theories of mathematical physics is presented in the book Teoria della elasticità by Enrico Betti. The book is interesting not only for the particular results found but also for its structure which became paradigmatic for the development of subsequent texts on elasticity, not only those in Italian. Betti’s interest was concentrated on the mathematical aspects of a physical theory. Physical principles are not discussed; they are only exposed in the most formal way possible. The objective is to arrive, without discussing epistemological or empirical problems, at the formulation and solution of differential equations that rule elasticity, as had become classic in the emerging mathematical physics. Beltrami wrote no complete books on elasticity; however, his contribution to this field was perhaps more original than that of Betti. A similar consideration holds true for Volterra and Somigliana.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

The Dialectic Relation Between Physics and Mathematics in the XIXth CenturyMathematical Physics in Italy in the XIX Century: The Theory of Elasticity

Part of the History of Mechanism and Machine Science Book Series (volume 16)
Editors: Barbin, Evelyne; Pisano, Raffaele
Capecchi, Danilo
The Dialectic Relation Between Physics and Mathematics in the XIXth Century — Sep 4, 2012
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References (23)

Publisher
Springer Netherlands
Copyright
© Springer Science+Business Media Dordrecht 2013
ISBN
978-94-007-5379-2
Pages
59 –78
DOI
10.1007/978-94-007-5380-8_3
Publisher site
See Chapter on Publisher Site

Abstract

[In the second half of the nineteenth century there was in Italy an important group of mathematicians who focused their attention on mathematical physics. The most prominent of them were Enrico Betti, Eugenio Beltrami, Gregorio Ricci–Curbastro and some others (Vito Volterra, Carlo Somigliana and Tullio Levi Civita) whose activity persevered for many years in the twentieth century. In this article, I will write about the contribution of this group to the theory of elasticity. The best representative writing on continuum mechanics and elasticity as theories of mathematical physics is presented in the book Teoria della elasticità by Enrico Betti. The book is interesting not only for the particular results found but also for its structure which became paradigmatic for the development of subsequent texts on elasticity, not only those in Italian. Betti’s interest was concentrated on the mathematical aspects of a physical theory. Physical principles are not discussed; they are only exposed in the most formal way possible. The objective is to arrive, without discussing epistemological or empirical problems, at the formulation and solution of differential equations that rule elasticity, as had become classic in the emerging mathematical physics. Beltrami wrote no complete books on elasticity; however, his contribution to this field was perhaps more original than that of Betti. A similar consideration holds true for Volterra and Somigliana.]

Published: Sep 4, 2012

Keywords: Mathematical Physic; Internal Force; Virtual Work; Deformable Body; Virtual Displacement

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