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Laplace transform sqaured differential

  1. Feb 24, 2013 #1
    Hi

    I was wondering what the Laplace transform of a squared differential is.
    With that I mean the Laplace of (y' )^2 (this being y'*y' and not the second order derivative). So for example velocity squared.
     
  2. jcsd
  3. Feb 24, 2013 #2

    rbj

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    there is a lot of similarity between the Fourier Transform and the Laplace Transform. the F.T. is really just the L.T. with the real part of [itex] s = \sigma + i \omega [/itex] set to zero. try to answer the question regarding the F.T. and see if you can generalize.
     
  4. Feb 25, 2013 #3
    I don't know the exact form off the top of my head, but it will be an ugly convolution of the form:

    integral (s^2 F(a)F(a-s) da)
     
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