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MathGroup Archive 2007

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Re: Help with plotting and iterations

  • To: mathgroup at smc.vnet.net
  • Subject: [mg72821] Re: [mg72808] Help with plotting and iterations
  • From: Bob Hanlon <hanlonr at cox.net>
  • Date: Sun, 21 Jan 2007 05:33:29 -0500 (EST)
  • Reply-to: hanlonr at cox.net

result[p_]:=Module[{a=1/2,b=1/4,h=1/4,
        m,m1,z,t,t1,t2,b1,c,x,aa,bb},
      m=b/a;
      m1=Sqrt[1-m^2];
      z=(p-I*h);
      t=ArcSin[z];
      t1=Re[t];
      t2=-Im[t];
      b1=Cot[t1]^2+m^2*Sinh[t2]-m1;
      c=m1^2*Cot[t1]^2;
      x=Reduce[{x^2 - b1*x - c==0,x>=0},x]//
            Last//N;
      aa=ArcCot[Sqrt[x]];
      bb=ArcTan[Sqrt[x/m1]];
      {EllipticF[aa,m],EllipticF[bb,m1]}];

TableForm[Join[
    Table[Prepend[result[p],p],{p,0.01,0.99,0.01}],
    Table[Prepend[result[p],p],{p,1,10}]],
  TableHeadings->{None,{"p","Faa","Fbb"}}]

ParametricPlot[result[p], {p, 0.01, Pi},
    AxesLabel->{"Faa","Fbb"},ImageSize->432];


Bob Hanlon

---- ashesh <ashesh.cb at gmail.com> wrote: 
> 
> Hello All,
> 
> Need help in working with Mathematica to determine (result_aa,
> result_bb) values over a range of variable "p".
> 
> p = 0.01;
> 
> a = 0.5; b = 0.25; h = 0.25;
> m = b/a;
> m1 = Sqrt[1-m m];
> z = (p-i h)/b;   (z is complex and (i h) represents imaginary part)
> t = ArcSin[z];
> t1 = Re[t];
> t2 = -Im[t];
> b1 = Cot[t1]^2 + m^2*Sinh[t2]-m1;
> c = m1^2*Cot[t1]^2;
> Solve[x^2 - b1*x - c,x];
> x = x/. %
> x = Last[x];  {i need the positive root from the two}
> aa = ArcCot[Sqrt[x]];
> bb = Arctan[Sqrt[x/m1]];
> Faa = EllipticF[aa,m];
> Fbb = EllipticF[bb,m1];
> 
> result_aa(count) = Faa;
> result_bb(count) = Fbb;
> count = count+1
> 
> I would like to determine the values of Faa and Fbb over a range of p =
> 0.01 to 10 with increments of 0.01 till 1.0 and then an increment of 1,
> that is [0.01:0.01:1 2:1:10]
> 
> Finally, I would like to plot with result_aa along x-axis and result_bb
> along y-axis.
> 
> Hope some one can solve the above problem.
> 
> Ashesh
> 


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