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Taylor Expansion (multivar)

  1. Apr 10, 2009 #1
    1. The problem statement, all variables and given/known data
    I'm having a hard time following a taylor expansion that contains vectors...

    http://img9.imageshack.us/img9/9656/blahz.png [Broken]
    http://g.imageshack.us/img9/blahz.png/1/ [Broken]
    2. Relevant equations



    3. The attempt at a solution

    Here's how I would expand it:

    -GMR/R^3 - GMr/R^3 + 3GMR/R^5*(R + r) + 3GMR/R^5(r + R)
    So you take d/dR(R^2 + r^2 + 2r dot R)^5/2 and then take d/dr ?
    I am basing my knowledge of multidimensional expansions off of what wikipedia is telling me, but I can't quite see how that r dot R term comes about

    Anyone have any ideas?
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 11, 2009 #2

    tiny-tim

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    Hi roeb! :smile:

    Hint: the denominator is Re3(1 + 2Re.r/Re2 + o(r2))3/2 :wink:
     
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