Expression for velocity

[stealth]

Hey guys! Nice forum!

 

Here's my first question. How do we get this expression for the velocity:

 

[math]\dot\vec{r}=\dot{r}+\frac{l^2}{m^2r^2}[/math], where l is the angular impulse of force

 

I thought we could do it like this:

[math]{\vec{l}}^2=l^2=(\vec{r}\times{{m\dot\vec{r}}})^2=m^2{}r^2{\dot{\vec{r}}}^2-(\vec{r}\bullet{m\dot{\vec{r}}})^2[/math]

We can't simply write:[math]{\dot\vec{r}}^2={\dot{r}}^2[/math], since then l=0. But why? Which rule forbids that equality. Similarly we can't treat the scalar product above as we would wish to. So how should one proceed in this case?

 

Thanks

[Meir Achuz]

Your first eq. is wrong (besides the misprints).

The second equation is correct.