Galilean Mechanics and Thermodynamics of Continua

Nonfiction, Science & Nature, Mathematics
Cover of the book Galilean Mechanics and Thermodynamics of Continua by Géry de Saxcé, Claude Valleé, Wiley
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Author: Géry de Saxcé, Claude Valleé ISBN: 9781119058090
Publisher: Wiley Publication: January 7, 2016
Imprint: Wiley-ISTE Language: English
Author: Géry de Saxcé, Claude Valleé
ISBN: 9781119058090
Publisher: Wiley
Publication: January 7, 2016
Imprint: Wiley-ISTE
Language: English

This title proposes a unified approach to continuum mechanics which is consistent with Galilean relativity. Based on the notion of affine tensors, a simple generalization of the classical tensors, this approach allows gathering the usual mechanical entities — mass, energy, force, moment, stresses, linear and angular momentum — in a single tensor.

Starting with the basic subjects, and continuing through to the most advanced topics, the authors' presentation is progressive, inductive and bottom-up. They begin with the concept of an affine tensor, a natural extension of the classical tensors. The simplest types of affine tensors are the points of an affine space and the affine functions on this space, but there are more complex ones which are relevant for mechanics − torsors and momenta. The essential point is to derive the balance equations of a continuum from a unique principle which claims that these tensors are affine-divergence free.

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This title proposes a unified approach to continuum mechanics which is consistent with Galilean relativity. Based on the notion of affine tensors, a simple generalization of the classical tensors, this approach allows gathering the usual mechanical entities — mass, energy, force, moment, stresses, linear and angular momentum — in a single tensor.

Starting with the basic subjects, and continuing through to the most advanced topics, the authors' presentation is progressive, inductive and bottom-up. They begin with the concept of an affine tensor, a natural extension of the classical tensors. The simplest types of affine tensors are the points of an affine space and the affine functions on this space, but there are more complex ones which are relevant for mechanics − torsors and momenta. The essential point is to derive the balance equations of a continuum from a unique principle which claims that these tensors are affine-divergence free.

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