Differential Equation for the Orbit - Goldstein Chapter 3

[getPhysical()]

Hello,

A question here about Classical Mechanics, Goldstein (Ed. 3)

On page 87 you have expression 3.33 which goes something like

$$\[<br /> \frac{1}{r^2}\frac{d}{d\theta}\left(\frac{1}{mr^2}\frac{dr}{d\theta}\right)-\frac{l^2}{mr^3}=f(r)<br /> \]$$

I appear to end up with

$$\[<br /> \frac{l}{r^2}\frac{d}{d\theta}\left(\frac{l}{mr^2}\frac{dr}{d\theta}\right)-\frac{l^2}{mr^3}=f(r)<br /> \]$$

instead. Any clues?

 

[D H]

Your second equation is the correct expression for a central force f(r) (assuming that your m is the reduced mass). Are you sure you are not simply misreading Goldstein? The first equation is not even dimensionally correct. 1's and l's often look very much alike.