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Appendix A

The choice of the local coordinate frames  is given in Fig. (1.5). This figure also gives our conventions concerning the angles $
\vartheta _{i}$ and $\varphi _{i}$. The coordinate frame unit vectors are calculated according to

$\displaystyle \hat{e}^{x}(i)$ = $\displaystyle -\frac{1}{\sin \vartheta }\hat{r}_{i-1}+\frac{\cos
\vartheta }{\sin \vartheta }\hat{r}_{i}$ (1.47)
$\displaystyle \hat{e}^{y}(i)$ = $\displaystyle \frac{1}{\sin \vartheta }\hat{r}_{i-1}\times \hat{r}_{i}$ (1.48)
$\displaystyle \hat{e}^{z}(i)$ = $\displaystyle \hat{r}_{i}$ (1.49)

Figure 1.5: Local coordinate frames

W.J. Briels