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Change of variables of differential equation

  1. May 23, 2012 #1
    I have an equation that I am trying to change the variables of, it has the form;

    [tex]

    \frac{d}{dt} W = g \frac{\partial}{\partial y} U + h x \frac{\partial^2}{\partial y^2} Z

    [/tex]

    Where W, U and Z are my dependent variables (This equation is just one of 3 coupled equations but have written only the above in general form).

    I want to change the variables into a rotating frame, so;

    x -----> x' = x(0) cos(wt) + y(0) sin(wt)
    y -----> y' = -x(0) sin(wt) + y(0) cos(wt)

    When putting these into the top equation, obviously it is simple to replace the x and y's but how do I change the differentials w.r.t. y with the new variable?

    Thanks for any help :D
     
  2. jcsd
  3. May 23, 2012 #2
    So you have a change of variables that looks like:
    x'=x'(x,y,t)
    y'=y'(x,y,t)
    t'=t

    Chain rule:

    df/dy = df/dx' * dx'/dy + df/dy'*dy'/dy + df/dt'*dt'/dy= sin(wt)df/dx' +cos(wt)df/dy'

    Sorry, I'm not sure how to use latex here. d is supposed to mean a partial d.
     
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