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

$$\hat{e}^{x}(i) -\frac{1}{\sin \vartheta }\hat{r}_{i-1}+\frac{\cos \vartheta }{\sin \vartheta }\hat{r}_{i}$$ = (1.47)

$$\hat{e}^{y}(i) \frac{1}{\sin \vartheta }\hat{r}_{i-1}\times \hat{r}_{i}$$ = (1.48)

$$\hat{e}^{z}(i) \hat{r}_{i}$$ = (1.49)

  

Figure 1.5: Local coordinate frames