I am trying to graph the partials of two equations with respect to t, with both equations being implicit. I know I should be getting ellipses with the x-axis as the major axis.
k = 5;
h = 1/4;
w = 5;
A = 100;
g = 9.81;
u[t_, x_, y_] := g*k*A/w*(Tanh[k*h]*Sinh[k*y] + Cosh[k*y]) Cos[k*x - w*t]
v[t_, x_, y_] := g*A*k/w*(Tanh[k*h]*Cosh[k*y] + Sinh[k*y]) Sin[k*x - w*t]
uu[t_, x_, y_] := D[u[t, x, y], t]
vv[t_, x_, y_] := D[v[t, x, y], t]
Print[uu[t, x, y]]
Print[vv[t, x, y]]
ImplicitPlot[{uu[t, x, y], vv[t, x, y]}, {x, -1, 1}, {y, -1, 1}, {t == 1}]
I am just getting back:
ImplicitPlot[{-4905. Sin[
5 t - 5 x] (Cosh[5 y] + Sinh[5 y] Tanh[5/4]), -4905. Cos[
5 t - 5 x] (Sinh[5 y] + Cosh[5 y] Tanh[5/4])}, {x, -1, 1}, {y, -1,1}, {t == 1}]
I believe that I am correct in fixing a t and graphing different x and y's for each t, but I am not sure if this is how to approach this. Thank you
ContourPlot[{uu[t, x, y], vv[t, x, y]} /. t -> 1, {x, -1, 1}, {y, -1, 1}, Contours->5]
? $\endgroup$