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Homework Help: 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
     
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