- where TI(J) is second-order transformation matrix that can be found in Izzuddin [36]:\(T_{I(J)} = \left[ {\begin{array}{*{20}c} {1 - \frac{{(\theta_{Y}^{I(J)} + \theta_{Z}^{I(J)} )^{2} }}{2}} & { -{^{i}} \theta_{Z}^{I(J)} + \frac{{\theta_{X}^{I(J)} \theta_{Y}^{I(J)} }}{2}} & {\theta_{Y}^{I(J)} + \frac{{\theta_{X}^{I(J)} \theta_{Z}^{I(J)} }}{2}} \\ {\theta_{Z}^{I(J)} + \frac{{\theta_{X}^{I(J)} \theta_{Y}^{I(J)} }}{2}} & {1 - \frac{{(\theta_{X}^{I(J)} + \theta_{Z}^{I(J)} )^{2} }}{2}} & {-\theta_{X}^{I(J)} + \frac{{\theta_{Y}^{I(J)} \theta_{Z}^{I(J)} }}{2}} \\ { - \theta_{Y}^{I(J)} + \frac{{\theta_{X}^{I(J)} \theta_{Z}^{I(J)} }}{2}} & {\theta_{X}^{I(J)} + \frac{{\theta_{Y}^{I(J)} \theta_{Z}^{I(J)} }}{2}} & {1 - \frac{{(\theta_{X}^{I(J)} + \theta_{Z}^{I(J)} )^{2} }}{2}} \\ \end{array} } \right]\)
-
\(\theta_{X}^{I(J)}\), \(\theta_{Y}^{I(J)}\), \(\theta_{Z}^{I(J)}\), and are incremental rotations of node I (or J) about the global axes X, Y and Z respectively, they are given in the output at each step of the computation
-
ϕ
I(J) are angles between the vectors y
I(J) and
\(\bar{y}_{I(J)}\)
