Del operator subindex

fobos3 · #1 $Old$ November 3rd, 2009, 11:56 AM

If you have a conservative force $\textbf{F}=-\nabla V(\textbf{r})$

Here is what is written in my textbook.
If $\textbf{F}^{(e)}_i$ is an external force then
$\sum_i \int_1^2 \textbf{F}_i^{(e)} \cdot d\textbf{s}_i=-\sum_i \int_1^2 \nabla_i V_i \cdot d\textbf{s}_i=-\left. \sum_i V_i \right|_1^2$

What is the meaning of the subscript $i$ in $\nabla_i$ . The only think that comes to my mind is a covariant derivative which is totally out of context.

I understand that $\textbf{F}^{(e)}_i=-\nabla V_i$ but what is the purpose of the subindex of the del operator? I am not familiar with that notation.

Ruun · #2 $Old$ November 3rd, 2009, 02:57 PM

I think it means the particle with the label $i$