Rigid model equations

Subsections

For the rigid model, there is no motion so the rotation matrix is simply the identity matrix

R = $\displaystyle \begin{pmatrix} 1 & . & . \\ . & 1 & . \\ . & . & 1 \\ \end{pmatrix}$ .

(16.2)

Rigid frame order matrix

The frame order matrix is

Daeg⁽ⁿ⁾ = R^⊗n,

(16.3)

where surface normalisation factor is 1.

Rigid 1 degree frame order

The 1 degree frame order matrix with tensor rank-2 is the identity matrix

$\begin{subequations}\begin{align} \textrm{Daeg}^{(1)}&= R^{\otimes 1} , \\ &= \... ...& . \\ . & 1 & . \\ . & . & 1 \\ \end{pmatrix}. \end{align}\end{subequations}$

Rigid 2 degree frame order

The 2 degree frame order matrix with tensor rank-4 is the identity matrix

$\begin{subequations}\begin{align} \textrm{Daeg}^{(2)}&= R^{\otimes 2} , \\ &= \... ...& . & . & . & . & . & . & . & 1 \\ \end{pmatrix}. \end{align}\end{subequations}$

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