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MathGroup Archive 2005

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Re: Attempt to generalize a constant

  • To: mathgroup at smc.vnet.net
  • Subject: [mg57705] Re: [mg57684] Attempt to generalize a constant
  • From: Pratik Desai <pdesai1 at umbc.edu>
  • Date: Sun, 5 Jun 2005 04:17:47 -0400 (EDT)
  • References: <200506040704.DAA11779@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Narasimham wrote:

>F[t_,mu_]= mu*JacobiSN[t,mu^2] is a function between +/- 1  extreme
>limits.
>
>FindRoot[F[t,mu]==1, {mu,1,1.5},MaxIterations-> 100 ] works for given t
>= Pi/4, solution is (mu-> 2.1236).
>
>But when it is attempted  to make t as a variable to plot solutions for
>a range of t values in:
>
>ImplicitPlot[F[t,mu]==1,{mu,1,1.5},{t,Pi/6,Pi}], it does not compute
>fully.  TIA for any tips.
>
>  
>
Hi
I may be wrong about this, but the elliptic integral (functions)
have no closed form solution, as a result the idea of using t as a 
explicit variable may not work here.

I have tried using Table where I change the values of t using the 
iterator, Anyway here is my attempt, actually you can control the number 
of iteration in order to get a smoother plot by changing n (see below). 
Also I have used Mathematica syntax for the function
as
JacobiSN[u,m] instead of JacobiSN[t,mu^2], I think that is the reason 
why I get values that are squared of what you have

Here is the code
Clear[F, t, m, sol1]
n = 2
sol1 = Table[First[FindRoot[Sqrt[m]*JacobiSN[u, m] ==1, {m, 1, 1.5}, 
MaxIterations -> 100]], {u, Ï?/4, Ï?, Ï?/(n*12)}]
l = Length[sol1]
m1 = Range[Ï?/4, Ï?, Ï?/(n*12)] // N
dat = Table[{m1[[s]], m /. sol1[[s]]}, {s, 1, l}]
ListPlot[dat, PlotJoined -> True]


Hope this helps

Pratik

--
Pratik Desai
Graduate Student
UMBC
Department of Mechanical Engineering
Phone: 410 455 8134



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