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The Geometrical Language of Continuum Mechanics

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The Geometrical Language of Continuum Mechanics Synopsis

Epstein presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. Divided into three parts of roughly equal length, the book opens with a motivational chapter to impress upon the reader that differential geometry is indeed the natural language of continuum mechanics or, better still, that the latter is a prime example of the application and materialisation of the former. In the second part, the fundamental notions of differential geometry are presented with rigor using a writing style that is as informal as possible. Differentiable manifolds, tangent bundles, exterior derivatives, Lie derivatives, and Lie groups are illustrated in terms of their mechanical interpretations. The third part includes the theory of fiber bundles, G-structures, and groupoids, which are applicable to bodies with internal structure and to the description of material inhomogeneity. The abstract notions of differential geometry are thus illuminated by practical and intuitively meaningful engineering applications.

About This Edition

ISBN: 9780521198554
Publication date: 26th July 2010
Author: Marcelo (University of Calgary) Epstein
Publisher: Cambridge University Press
Format: Hardback
Pagination: 324 pages
Genres: Engineering: Mechanics of solids
Differential and Riemannian geometry
Classical mechanics
Maths for engineers