Universal Law of Gravitation described by complex functions

  • #1
coolbeans777
3
0
I didn't put this in any of the physics sections, because I'm only learning this as it pertains to complex analysis. This was just an example provided in a free complex analysis textbook. Basically what I'm asking is why for the law of gravitation, f = GMm/r(t)^2, and it equals the equation in the picture when described by complex functions.

http://i.minus.com/iblXBR9aafGTaZ.png [Broken]
 
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Answers and Replies

  • #2
Mute
Homework Helper
1,388
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It looks to me like they're just using the complex function z(t) = x(t) + iy(t) in place of a vector function r(t) = (x(t),y(t)). Since the only information you really care about is x(t) and y(t), the two representations will give you the same results.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
43,021
971
Yes. This only uses the fact that the complex plane has two real dimensions. It has nothing to do with the algebraic properties that distinguish the complex plane from R2
 

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