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Geometrical Language of Continuum Mechanics

ISBN-10: 1107617030

ISBN-13: 9781107617032

Edition: 2014

Authors: Marcelo Epstein

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Description:

This book presents the fundamental concepts of modern differential geometry within the framework of continuum mechanics. It is 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 materialization 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.
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Book details

Copyright year: 2014
Publisher: Cambridge University Press
Publication date: 1/2/2014
Binding: Paperback
Pages: 326
Size: 7.00" wide x 10.00" long x 0.75" tall
Weight: 1.276
Language: English