Can anyone show me how to find r(dot) of the following vector?
r = <x,y> + (lm)/(m+n)<cos(theta),sin(theta)>
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!