Can anyone show me how to find r(dot) of the following vector?

r= <x,y> + (lm)/(m+n)<cos(theta),sin(theta)>

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- Oct 8th 2011, 02:06 PMmezyFind r(dot)
Can anyone show me how to find r(dot) of the following vector?

**r**= <x,y> + (lm)/(m+n)<cos(theta),sin(theta)> - Oct 8th 2011, 02:51 PMPlatoRe: Find r(dot)
- Oct 9th 2011, 05:53 AMmezyRe: Find r(dot)
Sorry about that. Here is the complete question:

Two point masses $\displaystyle m_{1}$ and $\displaystyle m_{2}$ are joint together by a rigid light rod of lenth $\displaystyle \ell$. If the rod move on a vertical plane under the action of the earth's gravitational field only, show that the path of the center of mass is a parabola and the rod rotates about the center of mass at a uniform angular velocity.

The given information I have is:

$\displaystyle \vec{r_{1}} = <x,y> + \displaystyle{\frac{\ell m_{1}}{m_{1}+m_{2}}} <cos (\theta),sin (\theta)>$

and

$\displaystyle \vec{r_{2}} = <x,y> - \displaystyle{\frac{\ell m_{2}}{m_{1}+{m_{2}}} <cos (\theta),sin (\theta)>$

Prove that $\displaystyle \theta$ is cyclic.

To do this, the first step is to find $\displaystyle \dot{\vec{r_{1}}}$ and $\displaystyle \dot{\vec{r_{2}}}$ and use them to find the Euler-Lagrangian equation.

I hope that's a little more specific. I just need help finding $\displaystyle \dot{\vec{r_{1}}} $.

Thanks! - Oct 20th 2011, 06:13 PMHartlwRe: Find r(dot)