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9783540407348

Orientations and Rotations

by
  • ISBN13:

    9783540407348

  • ISBN10:

    3540407340

  • Format: Hardcover
  • Copyright: 2004-02-01
  • Publisher: Springer Verlag
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Summary

The book is a comprehensive account of orientations and rotations of three-dimensional objects. The author's interest in orientations stems from the field of crystallographic texture analysis ' a branch of knowledge concerned with orientations of crystallites constituting polycrystalline materials. 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 (robotic manipulators, spacecraft control, computer animation, limb or eye kinematics, etc.).

Table of Contents

Preliminaries
1(18)
Rotations as Displacements
1(4)
Composition of Rotations
5(2)
Improper Rotations
7(1)
Matrix Representation
8(2)
Formal Approach to Orthogonal Transformations
10(9)
Parameterizations
19(32)
Half-turns
19(1)
Cayley Transformation and Rodrigues Parameters
20(3)
Axis and Angle Parameters
23(4)
Euler Angles
27(3)
Cayley--Klein Parameters
30(5)
Quaternions
35(6)
Rotation Vector
41(3)
Rotation Matrix in Non--Cartesian Coordinate Systems
44(2)
Miller Indices
46(3)
Computational Properties of Parameterizations
49(2)
Geometry of the Rotation Space
51(22)
SO(3) as a Riemannian Manifold
52(9)
Exponential Mapping
61(3)
SO(3) as a Lie Group
64(6)
Integration on SO(3)
70(3)
More on Small Orientation Changes
73(8)
Vector of Infinitesimal Rotation
73(3)
Rotation Rate Field and Continuity Equation
76(1)
Short Excursion into Mechanics
77(4)
Some Statistical Issues
81(12)
Mean Orientation
81(5)
Distributions on the Rotation Manifold
86(4)
Generation of Orientations
90(2)
Comparing Smooth Orientation Functions
92(1)
Symmetry
93(22)
Finite Point Groups
93(2)
Crystallographic Point Groups
95(2)
Asymmetric Domains
97(7)
Asymmetric Domains in Rodrigues Space
104(11)
Misorientation Angle and Axis Distributions
115(14)
Misorientation Angle Distributions
116(8)
Distributions of Rotation Axes
124(5)
Crystalline Interfaces and Symmetry
129(6)
Symmetrically Equivalent Boundaries
129(2)
Boundary Distributions
131(4)
Crystallographic Textures
135(16)
Texture Components in Cubic--Orthorhombic Case
136(2)
Rational Orientation Relationships
138(4)
Coincident Sublattices
142(9)
Diffraction Geometry
151(14)
Elementary Relations
152(1)
Orientations of Individual Crystallites
152(7)
Orientation Distributions from Pole Figures
159(6)
Effective Elastic Properties of Polycrystals
165(24)
Definitions and Simplest Principles
165(8)
Perturbation Methods
173(14)
Related Issues
187(2)
References 189(8)
Index 197

Supplemental Materials

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