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Y,y' domain

  1. May 5, 2014 #1
    In the Euler-Lagrange equations y and y' are independent variables, while for a given curve y(x), they are related by the differential equation y=f(x)y'. If you draw arbitrary curves on the y,y'-plane, it is immediately clear that most curves do not correspond to a curve y(x), is it fruitful to consider this domain further?
    Why are y and y' independent variables? It looks like the y,y'-domain has a different name, perhaps the frequency domain?
  2. jcsd
  3. May 5, 2014 #2

    D H

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    It's called phase space. Frequency domain is a different beast. Apply a Fourier transform to ##y(t)## you'll get ##\hat y(\omega)##. (Note well: nomenclature varies!)
  4. May 5, 2014 #3
    Frequency domain occured to me because the solution of y=f(x)y' is y=exp(int(f(x))), the frequency is also an argument of an exponential function. Why are y and y' independent variables?
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