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Hey guys!

I've got a question. How do we get this expression for the velocity:

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

I thought we could do it like this:

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

m^2r^2{\dot\vec{r}}^2-(\vec{r}\bullet{m{\dot\vec{r}})^2[/itex]

We can't simply write:[itex]{\dot\vec{r}}^2={\dot{r}}^2[/itex], 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

I've got a question. How do we get this expression for the velocity:

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

I thought we could do it like this:

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

m^2r^2{\dot\vec{r}}^2-(\vec{r}\bullet{m{\dot\vec{r}})^2[/itex]

We can't simply write:[itex]{\dot\vec{r}}^2={\dot{r}}^2[/itex], 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

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