Question: Plot with spheroidal coordinates

Knowing the realations between cartesian ans shperoidal coordinates (x,y,z and v,u,w respectively)

 

 

the goal is to take the following graph:

 

 

 

This graphic consists of three planes (One with v=const, let's say v=2, the other one with u=const, let's say u=π/4 and the last one with w=const let's say w=π/4), of three coordinate lines (line v with u=π/4 and w=π/4, line u with v=2 and w=π/4 and finally line w with v=2 and u=π/4). I wrote the following code but an error occurs...

restart;
with(plots);
with(LinearAlgebra);
F := <2*cosh(1)*cos(x), 2*sinh(1)*sin(x)*sin(t), 2*sinh(1)*sin(x)*cos(t)>;
S1 := plot3d(F, x = -Pi/2 .. Pi/2, t = 0 .. 2*Pi, color = "Green");
F, 1.5*Normalize(diff(F, x), 2);
eval(%, {t = Pi/4, x = Pi/4});
A1 := arrow(%, color = red);
V1 := textplot3d(<`+`(`%%`), v^`0`>, align = {'above', 'right'}, font = [Roman, bold, 14]);
F, 1.5*Normalize(diff(F, t), 2);
eval(%, {t = Pi/4, x = Pi/4});
A2 := arrow(%, color = red);
V2 := textplot3d(<`+`(`%%`), u^`0`>, align = {'below'}, font = [Roman, bold, 14]);
G := <2*cosh(x)*cos(Pi/4), 2*sinh(x)*sin(Pi/4)*sin(t), 2*sinh(x)*sin(Pi/4)*cos(t)>;
S2 := plot3d(G, x = 0 .. 100, t = 0 .. 2*Pi, color = "Cyan");
G, 1.5*Normalize(diff(G, x), 2);
eval(%, {t = Pi/4, x = Pi/4});
A3 := arrow(%, color = red);
V3 := textplot3d(<`+`(`%%`), w^`0`>, align = {'above', 'left'}, font = [Roman, bold, 14]);
display(S1, S2, A1, A2, A3, V1, V2, V3, scaling = constrained, axes = framed, labels = [x, y, z]);
 

 

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