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Trying to derive equation for acceleration in spherical coordinate system

  1. Sep 20, 2011 #1
    1. The problem statement, all variables and given/known data
    I was trying to figure out how to derive acceleration in spherical coordinates, and I realized that I need to find the projection of each spherical unit vector [ e(r), e(θ), and e(φ)] onto each Cartesian unit vector [î, j, and k], but I'm not quite sure as to how to do that. It's pretty intuitive for me to calculate the projections of e(r), but the other components confuse me a bit.


    2. Relevant equations
    see attached image


    3. The attempt at a solution
    I've attached the work I've done so far as an image (I didn't mean for that ' near the î on the bottom to be there..) ntsOv.png
     
  2. jcsd
  3. Sep 23, 2011 #2
    http://en.wikipedia.org/wiki/Unit_vectors#Spherical_coordinates" are the unit vectors in the spherical coordinate system from wikipedia. Your [itex]\hat{e_r}[/itex] is given as [itex]\hat{r}[/itex], [itex]\hat{e_\theta}[/itex] is given as [itex]\hat{\theta}[/itex] and [itex]\hat{e_\phi}[/itex] is given as [itex]\hat{\psi}[/itex].

    It looks to me that your [itex]\hat{e_\theta}[/itex] is drawn incorrectly in the diagram. Is it drawn to go straight in to the page?
     
    Last edited by a moderator: Apr 26, 2017
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