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Topic: Inflection
Replies: 16   Last Post: Jun 19, 2014 1:07 PM

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Roland Franzius

Posts: 433
Registered: 12/7/04
Re: Inflection
Posted: Jun 18, 2014 2:18 PM
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Am 18.06.2014 19:39, schrieb John Smith:
> A recent thread about points of inflection reminded me of a function I
> encountered when I was a math student.
>
> The function had many points of inflection but it also had points, which I
> presume are also called inflection points, where the gradient was infinite
> (i.e tending to a vertical rather than horizontal line on an x,y graph).
>
> I remember the graph looking like a staircase with rounded edges but I have
> completely forgotten what the function was. It's possible I have not
> remembered it correctly due to it being so long ago.
>
> Can anyone tell me what this function was or give me a similar function?


A candidate is the elliptic integral of the first kind.

F(x,k) = int dphi 1/Sqrt(1-k sin^2 phi)

with k approaching 1 from below.

F represents the physical time as a function of the angle for a rotating
mathematical pendulum nearly stopping indefinitely long times at the
sequence of top dead centers phi= (2n+1) pi.

Try

alpha.wolfram.com

plot EllipticF[x,1-10^-14] for 0<x<7pi

Dirct URL

http://www.wolframalpha.com/input/?i=plot+EllipticF[x%2C1-10^-14]+for+0%3Cx%3C7pi

--

Roland Franzius



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