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Homework Help: Divergence operator in cylindrical & sherical

  1. Aug 12, 2010 #1
  2. jcsd
  3. Aug 12, 2010 #2
  4. Aug 12, 2010 #3
    The "Del" operator in any orthogonal curvilinear coordinates is:

    [tex]
    \widetilde{\bigtriangledown} =\left ( \frac{1}{h_{1}}\frac{\partial }{\partial u_{1}}, \frac{1}{h_{2}}\frac{\partial }{\partial u_{2}},\frac{1}{h_{3}}\frac{\partial }{\partial u_{3}} \right )
    [/tex]

    where:

    [tex]
    h_{1},h_{2},h_{3}
    [/tex]

    are the "scaling factors"

    and

    [tex]
    u_{1},u_{2},u_{3}
    [/tex]

    are the parametrization variables.


    Example in Spherical Coordinates:

    [tex]
    h_{r}=\left \| \frac{\partial \vec{r}}{\partial r} \right \|=\left \| \frac{1}{\bigtriangledown r} \right \|=
    \left \| \frac{1}{\left ( \frac{\partial r}{\partial x}, \frac{\partial r}{\partial y},\frac{\partial r}{\partial z} \right )} \right \|
    [/tex]
    *same idea for Theta and Phi...

    [tex]
    \widetilde{\bigtriangledown} =\left ( \frac{1}{1}\frac{\partial }{\partial r}, \frac{1}{r}\frac{\partial }{\partial \theta },\frac{1}{r sin(\theta) }\frac{\partial }{\partial \varphi } \right )
    [/tex]

    makes sense? :)
     
  5. Aug 13, 2010 #4
    thank you !
     
  6. Aug 13, 2010 #5

    vela

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    Wikipedia also usually a good resource to find these kinds of formulas collected in one place.
     
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