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

**References**:**Attempt to generalize a constant***From:*"Narasimham" <mathma18@hotmail.com>