1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper
    Education Advisor

    Wikipedia also usually a good resource to find these kinds of formulas collected in one place.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Divergence operator in cylindrical & sherical
  1. Divergence operator (Replies: 3)

Loading...