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Galilean transform

  1. Jan 21, 2013 #1
    1. The problem statement, all variables and given/known data
    If there is a change of variables:
    [tex](\vec x(t),t)\to (\vec u=\vec x+\vec a(t),\,\,\,v=t+b)[/tex] where [itex]b[/itex] is a constant.

    Suppose I wish to write the following expression in terms of a gradient in [itex](\vec u, v)[/itex]

    [tex]\nabla_\vec x f(\vec x,t)+{d^2\vec a\over dt^2}[/tex] How do I do that?



    2. Relevant equations
    Please see above.


    3. The attempt at a solution
    For the first term, I think
    [tex]f(\vec x, t)\to f(\vec u -\vec a, v-b)[/tex]
    I am not sure what to do with the second term though.
     
  2. jcsd
  3. Jan 22, 2013 #2
    You should use chain rule I think, so

    [itex]\frac{\partial }{\partial x}=\frac{\partial u}{\partial x}\frac{\partial}{\partial u}[/itex]

    If I understood your question, this is what you are looking for.
     
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