Differential geometry and kinematics of continua:
Preface; Contents; 1. Introduction; 1.1 Motivation, Objectives, and Scope; 1.2 Historical Remarks; 1.3 Notation; 1.4 Summary; 2. Geometric Fundamentals; 2.1 Configurations, Coordinates, and Metrics; 2.1.1 Motion and coordinates; 2.1.2 Metric tensors; 2.1.3 Shifter tensors; 2.2 Linear Connections; 2....
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Buch |
| Sprache: | Englisch |
| Veröffentlicht: |
New Jersey [u.a.]
World Scientific
2015
|
| Schlagwörter: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027510472&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Zusammenfassung: | Preface; Contents; 1. Introduction; 1.1 Motivation, Objectives, and Scope; 1.2 Historical Remarks; 1.3 Notation; 1.4 Summary; 2. Geometric Fundamentals; 2.1 Configurations, Coordinates, and Metrics; 2.1.1 Motion and coordinates; 2.1.2 Metric tensors; 2.1.3 Shifter tensors; 2.2 Linear Connections; 2.2.1 Connection coefficients and covariant derivatives; 2.2.2 Torsion and curvature; 2.2.3 Identities for connection coefficients and curvature; 2.2.4 Riemannian geometry; 2.2.5 Euclidean space; 2.3 Differential Operators and Related Notation; 2.3.1 Gradient, divergence, curl, and Laplacian 2.3.2 Partial and total covariant derivatives2.3.3 Generalized scalar products; 3. Kinematics of Integrable Deformation; 3.1 The Deformation Gradient and Derived Quantities; 3.1.1 Deformation gradient; 3.1.2 Jacobian determinant; 3.1.3 Rotation, stretch, and strain; 3.1.4 Displacement; 3.1.5 Displacement potential; 3.1.6 Compatibility conditions; 3.1.7 Nanson's formula; 3.2 Integral Theorems; 3.2.1 Gauss's theorem; 3.2.2 Stokes's theorem; 3.3 Velocities and Time Derivatives; 3.3.1 Velocity fields; 3.3.2 Material time derivatives; 3.3.3 Lie derivatives; 3.3.4 Reynolds transport theorem 3.4 Coordinate Systems3.4.1 Cartesian coordinates; 3.4.2 Cylindrical coordinates; 3.4.3 Spherical coordinates; 3.4.4 Convected coordinates; 4. Geometry of Anholonomic Deformation; 4.1 Anholonomic Spaces and Geometric Interpretation; 4.1.1 Two-term decomposition of deformation gradient; 4.1.2 Anholonomicity conditions and partial differentiation; 4.1.3 Anholonomic basis vectors and metric tensors; 4.1.4 Convected anholonomic connection coefficients; 4.1.5 Integrable connections; 4.1.6 Contortion; 4.2 Anholonomic Covariant Derivatives; 4.2.1 Differentiation |
| Umfang: | IX, 182 S. |
| ISBN: | 9789814616034 |
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| 520 | |a Preface; Contents; 1. Introduction; 1.1 Motivation, Objectives, and Scope; 1.2 Historical Remarks; 1.3 Notation; 1.4 Summary; 2. Geometric Fundamentals; 2.1 Configurations, Coordinates, and Metrics; 2.1.1 Motion and coordinates; 2.1.2 Metric tensors; 2.1.3 Shifter tensors; 2.2 Linear Connections; 2.2.1 Connection coefficients and covariant derivatives; 2.2.2 Torsion and curvature; 2.2.3 Identities for connection coefficients and curvature; 2.2.4 Riemannian geometry; 2.2.5 Euclidean space; 2.3 Differential Operators and Related Notation; 2.3.1 Gradient, divergence, curl, and Laplacian | ||
| 520 | |a 2.3.2 Partial and total covariant derivatives2.3.3 Generalized scalar products; 3. Kinematics of Integrable Deformation; 3.1 The Deformation Gradient and Derived Quantities; 3.1.1 Deformation gradient; 3.1.2 Jacobian determinant; 3.1.3 Rotation, stretch, and strain; 3.1.4 Displacement; 3.1.5 Displacement potential; 3.1.6 Compatibility conditions; 3.1.7 Nanson's formula; 3.2 Integral Theorems; 3.2.1 Gauss's theorem; 3.2.2 Stokes's theorem; 3.3 Velocities and Time Derivatives; 3.3.1 Velocity fields; 3.3.2 Material time derivatives; 3.3.3 Lie derivatives; 3.3.4 Reynolds transport theorem | ||
| 520 | |a 3.4 Coordinate Systems3.4.1 Cartesian coordinates; 3.4.2 Cylindrical coordinates; 3.4.3 Spherical coordinates; 3.4.4 Convected coordinates; 4. Geometry of Anholonomic Deformation; 4.1 Anholonomic Spaces and Geometric Interpretation; 4.1.1 Two-term decomposition of deformation gradient; 4.1.2 Anholonomicity conditions and partial differentiation; 4.1.3 Anholonomic basis vectors and metric tensors; 4.1.4 Convected anholonomic connection coefficients; 4.1.5 Integrable connections; 4.1.6 Contortion; 4.2 Anholonomic Covariant Derivatives; 4.2.1 Differentiation | ||
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Datensatz im Suchindex
| _version_ | 1819350673219649536 |
|---|---|
| adam_text | Titel: Differential geometry and kinematics of continua
Autor: Clayton, John D
Jahr: 2015
Contents
Preface v
1. Introduction 1
1.1 Motivation, Objectives, and Scope..........................1
1.2 Historical Remarks............................................3
1.3 Notation........................................................4
1.4 Summary......................................................5
2. Geometric Fundamentals 7
2.1 Configurations, Coordinates, and Metrics ..................7
2.1.1 Motion and coordinates..............................7
2.1.2 Metric tensors........................................10
2.1.3 Shifter tensors........................................13
2.2 Linear Connections............................................14
2.2.1 Connection coefficients and covariant derivatives . 14
2.2.2 Torsion and curvature................................16
2.2.3 Identities for connection coefficients and curvature 17
2.2.4 Riemannian geometry................................20
2.2.5 Euclidean space......................................21
2.3 Differential Operators and Related Notation................27
2.3.1 Gradient, divergence, curl, and Laplacian..........27
2.3.2 Partial and total covariant derivatives..............29
2.3.3 Generalized scalar products..........................31
3. Kinematics of Integrable Deformation 33
3.1 The Deformation Gradient and Derived Quantities .... 33
vii
Differential Geometry and Kinematics of Continua
3.1.1 Deformation gradient................................33
3.1.2 Jacobian determinant................................38
3.1.3 Rotation, stretch, and strain........................45
3.1.4 Displacement..........................................49
3.1.5 Displacement potential..............................50
3.1.6 Compatibility conditions............................51
3.1.7 Nanson s formula ....................................53
3.2 Integral Theorems ............................................53
3.2.1 Gauss s theorem......................................54
3.2.2 Stokes s theorem......................................56
3.3 Velocities and Time Derivatives..............................58
3.3.1 Velocity fields ........................................58
3.3.2 Material time derivatives............................58
3.3.3 Lie derivatives........................................67
3.3.4 Reynolds transport theorem ........................67
3.4 Coordinate Systems ..........................................68
3.4.1 Cartesian coordinates................................68
3.4.2 Cylindrical coordinates..............................73
3.4.3 Spherical coordinates................................82
3.4.4 Convected coordinates................................90
Geometry of Anholonomic Deformation 93
4.1 Anholonomic Spaces and Geometric Interpretation .... 93
4.1.1 Two-term decomposition of deformation gradient. 93
4.1.2 Anholonomicity conditions and partial differentiation 95
4.1.3 Anholonomic basis vectors and metric tensors . . 97
4.1.4 Convected anholonomic connection coefficients . . 102
4.1.5 Integrable connections................................108
4.1.6 Contortion............................................Ill
4.2 Anholonomic Covariant Derivatives..........................114
4.2.1 Differentiation........................................114
4.2.2 Anholonomic connection coefficients................118
4.2.3 Total covariant derivatives..........................127
4.2.4 Divergence, curl, and Laplacian ....................132
4.2.5 Anholonomic cylindrical coordinates................136
Kinematics of Anholonomic Deformation 139
5.1 Multiplicative Kinematics....................................139
Contents ix
5.1.1 Jacobian determinants................................139
5.1.2 Nanson s formula ....................................149
5.1.3 Rotation, stretch, and strain........................150
5.1.4 Rate equations........................................155
5.2 Integral Theorems ............................................161
5.2.1 Domain transformations..............................161
5.2.2 Gauss s theorem......................................161
5.2.3 Stokes s theorem......................................162
5.2.4 Reynolds transport theorem........................165
Appendix A List of Symbols 169
Bibliography 177
Index 181
|
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| id | DE-604.BV042069758 |
| illustrated | Not Illustrated |
| indexdate | 2024-12-20T17:01:28Z |
| institution | BVB |
| isbn | 9789814616034 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027510472 |
| oclc_num | 896214568 |
| open_access_boolean | |
| owner | DE-384 DE-83 DE-19 DE-BY-UBM DE-29T |
| owner_facet | DE-384 DE-83 DE-19 DE-BY-UBM DE-29T |
| physical | IX, 182 S. |
| publishDate | 2015 |
| publishDateSearch | 2015 |
| publishDateSort | 2015 |
| publisher | World Scientific |
| record_format | marc |
| spellingShingle | Clayton, John D. 1976- Differential geometry and kinematics of continua Calculus of tensors Continuum mechanics Field theory (Physics) Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| subject_GND | (DE-588)4012248-7 (DE-588)4032296-8 |
| title | Differential geometry and kinematics of continua |
| title_auth | Differential geometry and kinematics of continua |
| title_exact_search | Differential geometry and kinematics of continua |
| title_full | Differential geometry and kinematics of continua John D. Clayton |
| title_fullStr | Differential geometry and kinematics of continua John D. Clayton |
| title_full_unstemmed | Differential geometry and kinematics of continua John D. Clayton |
| title_short | Differential geometry and kinematics of continua |
| title_sort | differential geometry and kinematics of continua |
| topic | Calculus of tensors Continuum mechanics Field theory (Physics) Geometry, Differential Differentialgeometrie (DE-588)4012248-7 gnd Kontinuumsmechanik (DE-588)4032296-8 gnd |
| topic_facet | Calculus of tensors Continuum mechanics Field theory (Physics) Geometry, Differential Differentialgeometrie Kontinuumsmechanik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027510472&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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