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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)
    t=t'
    f=f(x,t)

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

    df/dt'=df/dt+V*(df/dx)
    df/dx'=df/dx

    Am I correct?

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

    dg'/dt'+v'*(dg'/dx')
    dv'/dt'+v'*(dv'/dx')

    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:
    dg/dt-V*(dg/dx)
    dv/dt-V'*(dv/dx')

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

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