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MathGroup Archive 2012

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InverseFunction: how to manage?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg124268] InverseFunction: how to manage?
  • From: "Dr. Wolfgang Hintze" <weh at snafu.de>
  • Date: Sat, 14 Jan 2012 17:17:21 -0500 (EST)
  • Delivered-to: l-mathgroup@mail-archive0.wolfram.com

I apologize for asking this very elementary question but how do I 
manage InverseFunction?

Here is an example

When I solve the equation of motion for a pendulum

    f''[t] == Cos[f[t]], f[0]== 0, f'[0] == 0

I get (with paper and pencil) the time t as a function of the angle f 
thus

    t[f_] = Integrate[1/Sqrt[Sin[u]], {u, 0, f}]
    Out[22]=
    2*(EllipticF[f/2 - Pi/4, 2] + EllipticF[Pi/4, 2])

Now I want the the angle as a function of time (f[t]) like this

    "f[t_] = InverseFunction[t[f]]"

But this does not work. I also tried to define t as a pure function

t = 2*(EllipticF[#1/2 - Pi/4, 2] + EllipticF[Pi/4, 2]) &

but again, I have not seen a way to invert this, and for instance carry 
out Plot[f,{t,0,2 Pi}].

Thanks in advance for any hints.

Best regards,
Wolfgang






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