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Distance

Distance is defined by points $i$ and $j$:

\begin{displaymath}
d = \sqrt{\vec{r}_{ij} \cdot \vec{r}_{ij}} = \vert\vec{r}_{ij}\vert = r_{ij}
\end{displaymath} (7.14)

where
\begin{displaymath}
\vec{r}_{ij} = \vec{r}_i - \vec{r}_j \; .
\end{displaymath} (7.15)

The first derivatives of $d$ with respect to Cartesian coordinates are:

$\displaystyle \frac{\partial d} {\partial \vec{r}_i}$ $\textstyle =$ $\displaystyle \frac{\vec{r}_{ij}}{\vert\vec{r}_{ij}\vert}$ (7.16)
$\displaystyle \frac{\partial d} {\partial \vec{r}_j}$ $\textstyle =$ $\displaystyle -\frac{\partial d} {\partial \vec{r}_i}$ (7.17)



Bozidar BJ Jerkovic 2001-12-21