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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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