- #1

_Kenny_

- 4

- 1

## Homework Statement

I'm trying to do a little review of Lagrangian Mechanics through studying the two-body problem for a radial force. I have the Lagrangian of the system [tex] L=\frac{1}{2}m_1\dot{\vec{r_1}}^{2}+\frac{1}{2}m_2\dot{\vec{r_2}}^{2}-V(|{\vec{r_1}-\vec{r_2}}|) [/tex]. Now I'm trying to find the Euler-Lagrange Equations for [itex] r_1 [/itex] and [itex] r_2 [/itex] but I'm confused about taking the derivative of the potential portion with respect to either [itex] r_1 [/itex] or [itex] r_2 [/itex]. Please call me stupid and then tell me why I'm being stupid here.

## Homework Equations

[tex] L=\frac{1}{2}m_1\dot{\vec{r_1}}^{2}+\frac{1}{2}m_2\dot{\vec{r_2}}^{2}-V(|{\vec{r_1}-\vec{r_2}}|) [/tex]

[tex] \frac{dL}{dq}=\frac{d}{dt}\frac{dL}{d\dot{q}} [/tex]

[/B]

## The Attempt at a Solution

[tex] \frac{\partial L}{\partial r_1}=-\frac{\partial V(|{\vec{r_1}-\vec{r_2}}|)}{\partial r_1}=...? [/tex][/B]