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Equation of evolute?

  1. Jan 16, 2005 #1
    Ok, so i need to calculate the equation of the evolute for the catenary
    [tex]\gamma(t)= (t,cosh(t))[/tex].
    I'm not really sure how to do this, the definition of evolute I have requires a unit-speed parametrization, but it looks a little difficult to find that also (the arclength if i'm correct is given by
    [tex]s(t)=\frac{1}{2}(sin(2t)+t)[/tex]).

    Is there some "standard" way of finding the evolute?
     
  2. jcsd
  3. Jan 16, 2005 #2

    HallsofIvy

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    You are NOT correct about the arclength (did you confuse cosh(t) with cos(t)?).

    if [itex]\gamma(t)= (t, cosh(t))[/itex] then the arclength is given by [tex]\integral\sqrt{1+ sinh^2(t)}dt= \integral cosh(t)dt= sinh(t)[/itex].
     
  4. Jan 21, 2005 #3
    Yeah, i made a boo boo calculating the arclength :redface: . And apparently the definition i was given for the evolute of a unit-speed curve can also be used for any other parametrization of the curve, so everything's a-okay. :smile:
     
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