I have the following Lagrangian:
$$L=\frac{\mu}{2}\left(\dot{r}^2+r^2\dot\phi^2\right)-U(r),$$
The Euler-Lagrange equations are thus:
$$\frac{d}{dt}\left(\mu r^2\dot\phi\right)=0$$ $$\frac{d}{dt}(\mu \dot r)=\mu r\dot{\phi}^2-\frac{\partial}{\partial r}U(r).$$
I am trouble understanding what each Euler-Lagrange equation represent:
For example the first one: $\frac{d}{dt}\left(\mu r^2\dot\phi\right)=0$
What does $\mu r^2\dot\phi\ $ means?
Would it be the angular momentum?