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Galilean Transformation and Substantial Derivative

  1. Oct 6, 2006 #1
    I'm having trouble with the 2nd part of this problem. By letter "d" I mean "partial," I wasn't able to preview latex, so I went without it.

    x=x'+V*t' (V is a constant)

    Part a
    Find df/dt' and df/dx'. I got the following:


    Am I correct?

    Part b
    Consider substantial derivatives of density "g" and velocity "v" (which are also function of time and space), which are:


    Show that substantial derivatives have the same form when transformed into the x,t coordinate system (g'=g, v'=v-V).

    What I get is not of the same form:

    My problem is in the setup of this problem. How do I start?

  2. jcsd
  3. Aug 26, 2011 #2
    Hi, How did you solve the df/dx' part....???
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