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Slow-motion approach

  1. May 22, 2006 #1
    Hello i didn,t understand the slow motion approach of course i know that:

    [tex] \frac{\partial f }{\partial x^{0}}\sim \epsilon \frac{\partial f }{\partial x^{a}} [/tex] according to this approach with epsilon<<<1 small parameter for every smooth function my doubts are.

    a)what would happen to higher derivatives of f with respect to time and spatial coordinates?..x,y,z ?

    b)If we only want effect upto first order in epsilon parameter then..what would happen to:

    [tex] \nabla ^{2}f [/tex] (Laplacian)

    [tex] (1,1,1)*Gra(f) [/tex] (scalar product involving the gradient)

    or if we had [tex] \epsilon div(f) [/tex] would it mean that the only term that should be kept is df/dt if we consider effects only to first order?..

    thanks.:redface: :redface: :redface:
     
  2. jcsd
  3. May 22, 2006 #2

    pervect

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    Staff Emeritus
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    I've been trying to fill in the context of this post, with little success. Regarding what problem are you taking a "slow motion" approach? Are you doing low-velocity, weak-field approximations to GR?
     
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