
Understanding Quaternions
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Content
- Intro
- UNDERSTANDING QUATERNIONS
- UNDERSTANDING QUATERNIONS
- CONTENTS
- PREFACE
- Chapter 1MATHEMATICAL BASICS AND APPLICATIONSOF QUATERNIONS
- ABSTRACT
- INTRODUCTION
- QUATERNION ALGEBRA
- Basic Concepts
- Quaternion Operations
- QUATERNIONS AND OTHER MATHEMATICALREPRESENTATIONS
- Euler Angles and Quaternions
- Rodrigues's Rotation Formula and Quaternions
- Euler Parameters and Quaternions
- Cayley-Klein Parameters and Quaternions
- Modified Rodrigues Parameters and Quaternions
- APPLICATIONS OF QUATERNIONS
- Advantages of the Application of Quaternions in Representations ofRotations
- Estimation of Quaternions
- CONCLUSION
- REFERENCES
- Chapter 2UNDERSTANDING QUATERNIONS FROMMODERN ALGEBRAAND THEORETICAL PHYSICS
- Abstract
- 1. INTRODUCTION
- 2. QUATERNIONS AND SYMPLECTIC VECTOR SPACE
- 3. QUATERNIONS AND CLIFFORD ALGEBRA
- 4. GRASSMANN MANIFOLDS OVER QUATERNIONFIELDS
- 5. HOLONOMY GROUP AND QUATERNION
- 6. QUATERNIONS IN NON-COMMUTATIVEGEOMETRY AND QUANTUM GROUPS
- 7. SUMMARY AND DISCUSSION
- ACKNOWLEDGMENT
- REFERENCES
- Chapter 3SOLUTIONS WITH SPHERICAL SYMMETRYOF THE EQUATION FOR A SPIN 3/2 PARTICLE
- Abstract
- 1. INTRODUCTION
- 2. SYSTEM OF EQUATIONS AND SPHERICALSYMMETRY
- 3. SEPARATING THE VARIABLES
- 4. SEPARATING THE VARIABLES AND ADDITIONALCONSTRAINTS
- 5. SOLVING EQUATIONS FOR FUNCTIONS f0, g0
- 6. THE MATRIX FORM OF THE MAIN SYSTEM
- 7. THE CASE OF MINIMAL VALUE j = 1/2
- 8. STUDYING GENERAL CASE j = 3/2, 5/2, ...
- 9. FURTHER SPECIFYING SOLUTIONS
- 10. ACCOUNTING FOR ALGEBRAIC ANDDIFFERENTIAL CONSTRAINTS
- 11. CONCLUSION
- REFERENCES
- Chapter 4SPINOR MAXWELL EQUATIONS INRIEMANNIAN SPACE-TIME AND MODELINGCONSTITUTIVE RELATIONS
- Abstract
- 1. INTRODUCTION
- 2. MAXWELL EQUATIONS, SPINORS ANDQUATERNIONS
- 3. SEPARATING THE VARIABLES IN DE SITTER LIKEMODELS
- 4. SOLUTIONS IN MINKOWSKI SPACE
- 5. SOLUTIONS IN DE SITTER SPACE
- 6. SOLUTIONS IN ANTI DE SITTER MODEL
- 7. MAXWELL EQUATION IN SCHWARZSCHILD METRIC
- 8. SOLUTIONS IN SPHERICAL RIEMANN SPACE
- 9. SOLUTIONS IN LOBACHEVSKY SPACE
- 10. SOLUTIONS WITH CYLINDRIC SYMMETRY INSPHERICAL RIEMANN SPACE
- 11. RIEMANNIAN GEOMETRY AND MODELING THECONSTITUTIVE RELATIONS FOR SPECIAL MEDIA
- REFERENCES
- Chapter 5APPLICATIONS FOR RIGID BODY MOTIONPREDICTIONS WITH CFD
- Abstract
- 1. INTRODUCTION
- 2. COMPUTATIONAL METHODS
- 2.1. Governing Equations
- 2.2. MultiphaseMethod
- 2.3. 6DofMotion Solver
- 3. NUMERICAL RESULTS AND DISCUSSIONS
- 3.1. Water Entry of a Free Falling Sphere
- 3.2. Trim and Sinkage Prediction
- CONCLUSION
- ACKNOWLEDGMENT
- REFERENCES
- Chapter 6APPLICATIONS FOR THE BALLAST-FLIGHT
- Abstract
- 1. INTRODUCTION
- 2. GOVERNING EQUATIONS
- 3. SIMULATION RESULTS
- 3.1. Velocity of Ice Block
- 3.2. Shape of Ice Block
- CONCLUSION
- REFERENCES
- Chapter 7APPLICATIONS FOR THE STABILITY OFCAISSON-TYPE BREAKWATERS
- Abstract
- 1. INTRODUCTION
- 2. MATHEMATICAL FORMULATION
- 3. SIMULATION RESULTS
- 3.1. Solution Behavior with Breakwater Slope
- 3.2. Solution Behavior with Blocks Shapes
- CONCLUSION
- REFERENCES
- ABOUT THE EDITORS
- INDEX
- Blank Page
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