The geometrical language of continuum mechanics / Marcelo Epstein.

Format:

Book

Author/Creator:

Epstein, M. (Marcelo), author.

Language:

English

Subjects (All):

Continuum mechanics.

Physical Description:

1 online resource (xii, 312 pages) : digital, PDF file(s).

Place of Publication:

Cambridge : Cambridge University Press, 2010.

Language Note:

English

Summary:

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.

Contents:

Part I. Motivation and Background. The case for differential geometry

Vector and affine spaces

Tensor algebras and multivectors

Part II. Differential Geometry. Differentiable manifolds

Lie derivatives, Lie groups, Lie algebras

Integration and fluxes

Part III. Further Topics. Fibre bundles

Inhomogeneity theory

Connection, curvature, torsion

Appendix A. A primer in continuum mechanics.

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-139-88584-7

1-283-05196-6

9786613051967

1-139-04132-0

0-511-76267-4

1-139-04209-2

1-139-04472-9

1-139-03818-4

1-139-04054-5

OCLC:

710974862