Rotation, Reflection, and Frame Changes

Rotation, Reflection, and Frame Changes is an engineer’s practical resource for rotation-related theorems that might otherwise be difficult to find in literature. By providing extensive tutorials in requisite mathematics, intuitive insight, and computer source code, this work stands as a definitive contribution to engineering mechanics.

Whilst vast literature is available for the most common rotation-related tasks such as coordinate changes, most reference books tend to cover one or two methods, and resources for less-common tasks are scarce. Specialized research applications can be found in disparate journal articles, but a self-contained comprehensive review that covers both elementary and advanced concepts in a manner comprehensible to engineers is rare. Rotation, Reflection, and Frame Changes surveys a refreshingly broad range of rotation-related research that is routinely needed in engineering practice. By illustrating key concepts in computer source code, this book stands out as an unusually accessible guide for engineers and scientists in engineering mechanics.

1 Introduction
2 Notation and tensor analysis essentials
3 Orthogonal basis and coordinate transformations
4 Rotation operations
5 Axis and angle of rotation
6 Rotations contrasted with reflection
7 Quaternion representation of a rotation
8 Dyadic form of an invertible linear operator
9 Sequential rotations
10 Series expression for a rotation
11 Spectrum of a rotation
12 Polar decomposition
13 Strain measures
14 Remapping, advecting of interpolating rotations
15 Derivatives and rates of rotation
16 variations of a tensor-valued functions of scalars and vectors
17 Statistics of random orientation
18 Introduction to material and tensor symmetries
19 Frame indifference
20 Tensor symmetry
21 Scalar and invariants
22 PMFI for incremental constitutive models
23 Rigid Body Mechanics
23 Higher order rotations
24 Pseudo body force for spinning problems
25 Computer graphics visualization
26 Voigt and Mandel components
27 Higher order rotations
28 Closing remarks
A Code listings