Rotation, Reflection, and Frame Changes (eBook)

Dr Brannon is an ASME fellow with 25 years of experience in computational and theoretical mechanics, emphasizing high-rate destructive deformations of metals, ceramics, and rocks. Her models are applied to armor, ceramic hip replacements, bunker surety, and shaped-charge jet well-bore completion. She is also known for her monographs on mathematics.

1 Introduction2 Notation and tensor analysis essentials3 Orthogonal basis and coordinate transformations4 Rotation operations5 Axis and angle of rotation6 Rotations contrasted with reflection7 Quaternion representation of a rotation8 Dyadic form of an invertible linear operator9 Sequential rotations10 Series expression for a rotation11 Spectrum of a rotation12 Polar decomposition13 Strain measures14 Remapping, advecting of interpolating rotations15 Derivatives and rates of rotation16 variations of a tensor-valued functions of scalars and vectors17 Statistics of random orientation18 Introduction to material and tensor symmetries19 Frame indifference20 Tensor symmetry21 Scalar and invariants22 PMFI for incremental constitutive models23 Rigid Body Mechanics23 Higher order rotations24 Pseudo body force for spinning problems25 Computer graphics visualization26 Voigt and Mandel components27 Higher order rotations28 Closing remarksA Code listings