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Differential Equation for the Orbit - Goldstein Chapter 3

  1. May 2, 2010 #1
    Hello,

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

    On page 87 you have expression 3.33 which goes something like

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

    I appear to end up with

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

    instead. Any clues?
     
  2. jcsd
  3. May 2, 2010 #2

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    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.
     
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