Rotation vector components

The soft layer distortions si, s2, and s3 and together with the hard layer compression, give can be described by the rotation vector components. 

The voltage can also be pictured as a rotating vector with its own amphtude and frequency. Both current and potential can be represented as having real (observed) and imaginary (not observed) components. 

The components of the translation and rotation vectors are given as Tx> Ty, T and RX Ry, Rz, respectively. The components of the polarizability tensor appear as linear combinations such as axx + (xyy> etc, that have the symmetry of the indicated irreducible representation. 

Figure 5.3 Numerically simulated Stokes polarization vector components 5j (dashed line), 2 (solid line) and Sj (dotted line) versus propagation direction z- Frames (a) is foriV = 10 crystals, while frames (b) and (c) are for W = 30 and W = 100 crystals in a stack. In all cases, each crystal length is L, the rotary power is = k/5L, and the rotation angle in each crystal is = kx/4N with k being the number of the crystal in the row (k = 1,2,3,...

In the principal coordinates, of course, there are only three nonzero components of the stress and strain-rate tensors. Upon rotation, all nine (six independent) tensor components must be determined. The nine tensor components are comprised of three vector components on each of three orthogonal planes that pass through a common point. Consider that the element represented by Fig. 2.16 has been shrunk to infinitesimal dimensions and that the stress state is to be represented in some arbitrary orientation (z, r, 6), rather than one aligned with the principal-coordinate direction (Z, R, 0). We seek to find the tensor components, resolved into the (z, r, 6) coordinate directions. 

In the above equation (5.2) where X is the original vector represented by N components, Y is the new, rotated vector represented by the same number of components, while A is the rotation matrix. In the case of the Fourier transformation the rotation matrix A (eq. 5.2) is written as a matrix W ... 

Rewritten in terms of vector components Eq. (2.65) gives the three center of mass conditions, while Eq. (2.66) gives the three rotational constraints in a form similar to Eq. (2.45),... 

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