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Hamiltonian in cylindrical coordinates

  1. Aug 17, 2010 #1
    Hi, I'm trying to find the Hamiltonian for a system using cylindrical coordinates.

    I start of with the Lagrangian [tex] L=\frac{1}{2}m(\dot{r}^2+r^2\dot{\theta}^2+\dot{z}^2)-U(r,\theta,z) [/tex]

    From that, using [tex]H=\sum p\dot{q}-L[/tex]

    But the standard answer is

    So where did I go wrong?

    Thanks for any help :)
  2. jcsd
  3. Aug 17, 2010 #2


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    What did you use for pθ?

    Don't forget that

    [tex]p_j= \frac{\partial L}{\partial \dot{q}_j}.[/tex]
  4. Aug 17, 2010 #3
    Ah, of course!
    Kind of obvious really...

    Thanks for the help :)
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