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Problem with one transformation

  1. Oct 15, 2012 #1
    Hello.

    I don't understand one transformation that is made on page 25 of this paper:

    http://www.atm.ox.ac.uk/user/read/mechanics/LA-notes.pdf

    It is the second equation from the top, ont the one marked as '2', but just the second one.

    dx/dt*(\delta x*dx/dt)=1/2\delta(dx/dt)^2

    Why is that?
     
  2. jcsd
  3. Oct 15, 2012 #2

    haruspex

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    You've slightly misrepresented what the paper says. It's dx/dt*(δ dx/dt), not dx/dt*(δx dx/dt). To make it easier to read, let's write v for dx/dt. The transformation is then from v δv to δ(v2)/2. Is that clearer?
     
  4. Oct 15, 2012 #3
    Right, I've made a mistake during writing the equation. Unfortunately, the transformation I don't get is the one you wrote. It's probably sth. very basic and I can't figure it out :s.
     
  5. Oct 15, 2012 #4

    haruspex

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    Well, what do you get if you differentiate v2?
     
  6. Oct 15, 2012 #5
    Oh. My. God. I'm dumb, thanks.
     
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