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 06/28/12 7:24pm
Author later posted a longer version:
=====
I have a set of coupled Differential Equations:
\[Beta]'[t] == (Sqrt[3/2]*\[Alpha]^2*T[t]^(11/2))/m^(9/2)*(bb^2 - \[Beta][t]^2
T'[t] == (Sqrt[g]*T[t]^3)/(Sqrt[3]*M)
with these conditions:
M = 10000;
g = 1;
\[Alpha] = 1;
A = 10;
a = 0;(*initial plot temp*)
b = .001; (*final plot temp*)
c = .01; (*initial temp*)
d = 0; (*initial \[Beta]*)
m = .001;
*Although the limits a and b can be manipulated to show the results best.
What I want to do now not only solve this set of coupled differential equations but also generate a plot for \[Beta] as a function of T. I have B[t] and T[t] and what I want now is to generate a plot of B[t] from these equations.
I have tried this;
s = NDSolve[{\[Beta]'[t] == (Sqrt[3/2]*\[Alpha]^2*T[t]^(11/2))/m^(
9/2)*(bb^2 - \[Beta][t]^2),
T'[t] == (Sqrt[g]*T[t]^3)/(Sqrt[3]*M), \[Beta][0] == 0,
T[0] == c}, {\[Beta][t], T[t]}, {t, a, b}];
ParametricPlot[{(Evaluate[{T[t], \[Beta][t]} /. s])}, {t, a, b},
PlotRange -> Automatic]
But I can't seem to generate anything coherent.
Ideally this set of equations should regenerate the plots produced by:
M = 10000;
g = 1;
\[Alpha] = 1;
A = 10;
a = .01;(*initial plot temp*)
b = 1.2; (*final plot temp*)
c = 0.00000001; (*initial temp*)
d = 0; (*initial \[Beta]*)
m = 1;
bb = (g/(2*\[Pi])^(3/2)*(m/T)^(3/2)*E^(-m/T));
s = NDSolve[{\[Beta]'[T] == (3*\[Alpha]^2*M*T^(5/2))/(
Sqrt[2*g]*m^(9/2))*(bb^2 - \[Beta][T]^2), \[Beta][c] ==
d}, \[Beta], {T, a, b}, Method -> "BDF"];
Plot[{(Evaluate[\[Beta][T] /. s])/bb}, {T, a, b},
PlotRange -> Automatic]
Any and all help would be much appreciated!!!
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