Hello, I have a slightly complicated coupled differential equation here. I was wondering if I could actually get an approximate function to these graphs that NDSolve is producing. Moreover, can I use variable coefficients instead of the constants m and k I have on top? I’m trying to get a function where I can also vary the m and k coefficients.
Something like this perhaps?
g = 9.81; l0 = 0.2;
Manipulate[
sol = NDSolve[{x''[t] == (l0 + x[t])*(theta'[t])^2 - (k*x[t])/(m) +
g*Cos[theta[t]],
theta''[t] == (-2*theta'[t]*x'[t])/(l0 + x[t]) - (g*
Sin[theta[t]])/(l0 + x[t]), x[0] == 0.05, x'[0] == 0,
theta[0] == 0.35, theta'[0] == 0}, {x, theta}, {t, 0, 100}];
fx = x /. sol[[1, 1]];
ft = theta /. sol[[1, 2]];
pl1 = ParametricPlot[{t, fx[t]} /. sol, {t, 0, 40},
PlotRange -> {{0, 6}, {-1, 3}}];
pl2 = ParametricPlot[{t, ft[t]} /. sol, {t, 0, 40}];
Show[pl1, pl2],
{{m, .9}, 0, 2}, {{k, 10}, 0, 20}]
What do you mean by “approximate function to these graphs”?
Hello, NDSolve allows me to plot the graphs of these differential equations but can it also give me an algebraic equation where I can insert an x value and output a y value. furthermore, can I make it so that this equation has the variable coefficients I have mentioned above in it. Or is this just not possible.
NDSolve gives back InterpolationFunction - objects. In my code above I called them fx and ft.
Try ft[ 3.57 ]. This should give a number, the value of theta at t = 3.57. So you insert a value and get back another one.
Concerning variable coefficients you should check the documentation of ParametricNDSolveValue. My old version of Mma doesn’t have/know this functionality.
What do you mean by algebraic equation? Why do you need this? You have already fx[t] and ft[t].