Orientations and Rotations

From the reviews of the first edition: "Morawiec presents a ... detailed discussion of the geometry of the rotation space and corresponding elementary regions due to specific crystal or sample symmetries. ... A significant advantage of the book is, that it closes the gap between the formal analysis of orientations and continuum mechanics. ... a mathematically precise approach containing a large number of instructing and helpful problems and comments is given. Thus, this book is highly recommendable for students, engineers and scientists working in the field of crystallographic texture analysis." (T. Bohlke, Technische Mechanik, Vol. 26 (1), 2006) "The book gives an introduction to the techniques used in the description of crystallographic textures for the orientational relationships between the various parts. ... The text is very readable. Its approach is mathematical, but not abstract. ... The rather schematic treatment in the book of a cubic-orthorhombic case is the closest to the practical work. ... in total, the book presents a clear introduction to the basic mathematics needed for specifying the orientational relationships playing a role in the description of textures." (T.Janssen, Mathematical Reviews, 2006 b) "Essentially, Orientations and Rotations treats the mathematical and computational foundations of texture analysis. It contains an extensive and thorough introduction to parameterizations and geometry of the rotation space. Since the notions of orientations and rotations are of primary importance for science and engineering, the book can be useful for a very broad audience using rotations in other fields." (Zeitschrift fur Kristallographie, Issue 10, 2004) "The mathematics of orientation, which this book addresses in great detail, is ... very relevant to Earth Science. ... I will certainly use it as a reference. ... the book is a detailed and careful treatment of the topic which pulls together many pieces of work previously scattered through the literature, and makes a coherent whole." (John Wheeler, Geological Magazine, Vol. 143 (4), 2006)

• 1 Preliminaries.- 2 Parameterizations.- 3 Geometry of the Rotation Space.- 4 More on Small Orientation Changes.- 5 Some Statistical Issues.- 6 Symmetry.- 7 Misorientation Angle and Axis Distributions.- 8 Crystalline Interfaces and Symmetry.- 9 Crystallographic Textures.- 10 Diffraction Geometry.- 11 Effective Elastic Properties of Polycrystals.- References.