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Taylor Expansion (multivar)

  • Thread starter roeb
  • Start date
  • #1
107
1

Homework Statement


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]

Homework Equations





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?
 
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Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
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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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