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I was reading through the second edition of the book Galactic Dynamics from Binney and Tremaine.

Chapter 3 :eqns 3.8 and 3.9.

3.8 says

[tex]r^2 \frac{d \phi}{dt}=L=constant[/tex].

Then 3.9 writes

[tex]\frac{d}{dt}=\frac{L}{r^2}\frac{d}{d\phi}[/tex]

But is this correct? For example, if I act this on r, the radial coordinate, I get

[tex]\frac{dr}{dt}=0[/tex]

For a general orbit in a central force, r is not a constant.

So is there a mistake in the book, or am I missing something?