Chapter 12: Cartesian Tensor Transformation—Rotations

Kapitel in diesem Buch

1. Frontmatter i
2. Contents vii
3. Preface xiii
4. About the Author xv
5. Chapter 1: Introduction 1
6. Chapter 2: Coordinate Systems Definition 3
7. Chapter 3: Basis Vectors and Scale Factors 5
8. Chapter 4: Contravariant Components and Transformations 9
9. Chapter 5: Covariant Components and Transformations 13
10. Chapter 6: Physical Components and Transformations 15
11. Chapter 7: Tensors—Mixed and Metric 17
12. Chapter 8: Metric Tensor Operation on Tensor Indices 21
13. Chapter 9: Dot and Cross Products of Tensors 29
14. Chapter 10: Gradient Vector Operator—Christoffel Symbols 35
15. Chapter 11: Derivative Forms—Curl, Divergence, Laplacian 51
16. Chapter 12: Cartesian Tensor Transformation—Rotations 65
17. Chapter 13: Coordinate Independent Governing Equations 75
18. Chapter 14: Collection of Relations for Selected Coordinate Systems 89
19. Chapter 15: Rigid Body Rotation: Euler Angles, Quaternions, and Rotation Matrix 103
20. Chapter 16: Mechanical Stress Transformation: Analytical and Mohr’s Circle Methods 143
21. Chapter 17: The Worked Examples 191
22. Chapter 18: Exercises 219
23. References 227
24. Index 231