Rotation, Reflection, and Frame Changes
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Rotation, Reflection, and Frame Changes

Orthogonal tensors in computational engineering mechanics
Sofort lieferbar | Lieferzeit:3-5 Tage I
Rebecca M Brannon
IOP Expanding Physics
eBook Typ:
Adobe Digital Editions
eBook Format:
Adobe DRM [Hard-DRM]

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

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