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I Brachistochrone problem with friction

  1. May 18, 2017 #1
    I am doing some research on the brachistochrone problem WITH frictions. I found the following demonstration on the web.
    The beginning is ok. But I can't understand how the managed to pass between (29) and (30) and between (30) and ((32), (33)).

    If someone could help me, it would be very nice !
    thanks :)

    The link to the article : http://mathworld.wolfram.com/BrachistochroneProblem.html
  2. jcsd
  3. May 18, 2017 #2
    To go from 29 to 30, it is pretty clear that they have integrated one time. Eq(29) is second order while eq(30) is first order. What you need to do is convince yourself that 30 is indeed the result of integrating 29.
  4. May 19, 2017 #3
    Yeah, I got it !
    Tanks for your help Dr.D ! :smile:
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