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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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