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....

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Bibliographische Detailangaben
Beteilige Person: Clayton, John D. 1976- (VerfasserIn)
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