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I'm having a equation $\dfrac{d}{dt}=\dfrac{l}{mr^2}\dfrac{d}{d\varphi}$ which I'm supposed to substitute into $m\ddot{r}-\dfrac{l^{2}}{m r^{3}}=f(r)$ and have a differential equation $\dfrac{1}{r^2}\dfrac{d}{d\varphi}\left(\dfrac{1}{mr^2}\dfrac{dr}{d\varphi}\right)-\dfrac{l^2}{mr^3}=f(r)$ but somehow I just have a huge problem with it. Hope you can help me!

Matti Hokkanen
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    It helps if you add details, and what you attempted and where you got stuck. Otherwise people will waste time explaining things you already know or talking over your head. By the way, what happened to the $\mu$? I assume you have a definition for it. – RobertTheTutor Apr 03 '21 at 15:55
  • Thanks! The $\mu$ was typo I edited now.

    The best I

     – Matti Hokkanen Apr 03 '21 at 16:16
  • ...This is what I had: $m\ddot{r}=m(\dfrac{d}{dt}\dot{r}=m((\dfrac{l}{mr^2}\dfrac{d}{d\varphi})\dot{r})=m((\dfrac{l}{mr^2})(\dfrac{dr}{d\varphi}\dfrac{l}{mr^2})=\dfrac{l}{r^2}\dfrac{d}{d\varphi}(\dfrac{l}{mr^2}\dfrac{dr}{d\varphi})$. But I don't understand how I get rid of the l. I think that there's some spot I just don't notice. (sorry about my bad english). – Matti Hokkanen Apr 03 '21 at 16:26
  • I'm trying to look it up. Is this classical physics or quantum? – RobertTheTutor Apr 03 '21 at 16:50
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    Goldstein 2nd edition equations 3-12 to 3-33, right? – RobertTheTutor Apr 03 '21 at 16:58
  • Aha! The L is there in the equation, you mistook it for a 1. – RobertTheTutor Apr 03 '21 at 17:04
  • @RobertTheTutor Yes, that is the book and those the equations! Aren't those 1:s in the equation 3.33? – Matti Hokkanen Apr 03 '21 at 17:17
  • Nope, they are lowercase L's. Look closely and compare to the 1's in the equation on the next line. – RobertTheTutor Apr 03 '21 at 18:45
  • Nope, they are 1's :) and that's the problem how do I get rid of lower case L's. Just making sure that we're talking about same equation: $\dfrac{1}{r^2}\dfrac{d}{d\varphi}(\dfrac{1}{mr^2}\dfrac{dr}{d\varphi})-\dfrac{l^2}{mr^3}=f(r)$. – Matti Hokkanen Apr 04 '21 at 06:48
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    I'm looking at the 2nd edition, and in my copy both of the 1's you wrote are lowercase L's. Also my version has $\theta$ instead of $\varphi$. If you have a different edition, sounds like it has a typo in it! – RobertTheTutor Apr 04 '21 at 12:26
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    You can tell it can't be $1$'s because the units don't match otherwise, and this is a physics equation, the units have to match. – RobertTheTutor Apr 04 '21 at 12:28
  • Huge thanks to you! You should never trust the book but yourself :D – Matti Hokkanen Apr 06 '21 at 06:05

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