The geometrical language of continuum mechanics:
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...
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| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge
Cambridge University Press
2010
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| Subjects: | |
| Online Access: | BSB01 FHN01 Volltext |
| 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 |
| Item Description: | Title from publisher's bibliographic system (viewed on 05 Oct 2015) |
| Physical Description: | 1 online resource (xii, 312 pages) |
| ISBN: | 9780511762673 |
| DOI: | 10.1017/CBO9780511762673 |
Staff View
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| 520 | |a 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 | ||
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Record in the Search Index
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| any_adam_object | |
| author | Epstein, M. |
| author_facet | Epstein, M. |
| author_role | aut |
| author_sort | Epstein, M. |
| author_variant | m e me |
| building | Verbundindex |
| bvnumber | BV043945643 |
| classification_rvk | SK 370 UF 2000 |
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| 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 |
| ctrlnum | (ZDB-20-CBO)CR9780511762673 (OCoLC)967604591 (DE-599)BVBBV043945643 |
| dewey-full | 531 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 531 - Classical mechanics |
| dewey-raw | 531 |
| dewey-search | 531 |
| dewey-sort | 3531 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| doi_str_mv | 10.1017/CBO9780511762673 |
| format | Electronic eBook |
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| indexdate | 2024-07-10T07:39:24Z |
| institution | BVB |
| isbn | 9780511762673 |
| language | English |
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| spelling | Epstein, M. Verfasser aut The geometrical language of continuum mechanics Marcelo Epstein Cambridge Cambridge University Press 2010 1 online resource (xii, 312 pages) txt rdacontent c rdamedia cr rdacarrier Title from publisher's bibliographic system (viewed on 05 Oct 2015) 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 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 Continuum mechanics Differentialgeometrie (DE-588)4012248-7 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 gnd rswk-swf Kontinuumsmechanik (DE-588)4032296-8 s Differentialgeometrie (DE-588)4012248-7 s 1\p DE-604 Erscheint auch als Druckausgabe 978-0-521-19855-4 Erscheint auch als Druckausgabe 978-1-107-61703-2 https://doi.org/10.1017/CBO9780511762673 Verlag URL des Erstveröffentlichers Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Epstein, M. The geometrical language of continuum mechanics 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 Continuum mechanics Differentialgeometrie (DE-588)4012248-7 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4032296-8 |
| title | The geometrical language of continuum mechanics |
| title_auth | The geometrical language of continuum mechanics |
| title_exact_search | The geometrical language of continuum mechanics |
| title_full | The geometrical language of continuum mechanics Marcelo Epstein |
| title_fullStr | The geometrical language of continuum mechanics Marcelo Epstein |
| title_full_unstemmed | The geometrical language of continuum mechanics Marcelo Epstein |
| title_short | The geometrical language of continuum mechanics |
| title_sort | the geometrical language of continuum mechanics |
| topic | Continuum mechanics Differentialgeometrie (DE-588)4012248-7 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Continuum mechanics Differentialgeometrie Kontinuumsmechanik |
| url | https://doi.org/10.1017/CBO9780511762673 |
| work_keys_str_mv | AT epsteinm thegeometricallanguageofcontinuummechanics |