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!

Transformation from Cartesian to spherical polar coordinates

  1. Nov 29, 2011 #1
    Transformation from Cartesian to spherical polar coordinates

    In dimensions:

    x=r sinθ cos [itex]\varphi[/itex] and y= r sin θ sin [itex]\varphi[/itex] z=r cos θ

    Show one example of:

    ∂z[itex]\alpha[/itex]/ ∂xμ . ∂xμ/ ∂z[itex]\alpha[/itex] = δ[itex]\alpha[/itex][itex]\beta[/itex]

    Now here is my answer:

    δyx=(∂y/∂r . ∂r/∂x) + (∂y/∂θ . ∂θ/∂x) + (∂y/∂[itex]\varphi[/itex] . ∂[itex]\varphi[/itex]/∂x)



    Is this correct? If not where have I made an error... Thank you
     
  2. jcsd
  3. Jul 18, 2012 #2
    Re: Transformation

    Just like to pick up in this old thread, still having trouble with the question.

    Using what I have already done:

    δrθ=(∂r/∂x . ∂x/∂θ) + (∂r/∂y . ∂y/∂θ) + (∂r/∂z . ∂z/∂θ) (1)

    Where:

    x=r sin θ cos φ and y= r sin θ sin φ z= r cos θ

    Would (1) then become:

    δyx= = ((sin θ cos φ) . ( r cos θ cos φ)) + ((sin θ sin φ) . (cos θ sin φ)) + ((cos θ) . (-r sin θ))

    Then multiply out the brackets and simplify
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook