I have 3 implicit equations in 5 variables: f1(S, yh, yd, xh, J)=0, f2(S, yh, yd, xh, J)=0, and f3(S, yh, yd, xh, J)=0. These equations determine a 3D surface in S-yh-yd coordinate system. The equations are given below.
M = 1;
roo = 0.01;
xd = 3;
f1[S_, yh_, yd_, xh_, J_]:= 2 M (xh^2 - (yh + 1)^2)/(xh^2 + (yh + 1)^2)^2 +
2 S ((xh - xd)^2 - (yh + yd)^2)/((xh - xd)^2 + (yh + yd)^2)^2 +
J/(2 yh) == 0,
f2[S_, yh_, yd_, xh_, J_]:= M*xh (yh + 1)/(xh^2 + (yh + 1)^2)^2 +
S (xh - xd) (yh + yd)/((xh - xd)^2 + (yh + yd)^2)^2 == 0,
f3[S_, yh_, yd_, xh_, J_]:= J*Log[2 yh*J/roo] + 2 M (yh + 1)/(xh^2 + (yh + 1)^2) +
2 S (yh + yd)/((xh - xd)^2 + (yh + yd)^2) - (Log[2/roo] + 1) == 0,
where S, yh, yd, xh, J are Reals, yh>0, and yd>0.
I am trying to obtain the surface in the S-yh-yd coordinate system like the following image. How to plot it?
What I have tried: For 1 equation in 3 variables: f(S, yh, yd) = 0, I can use ContourPlot3D to get the surface; For equations expressed in an explicit form: S = S(xh, J), yh = yh(xh, J), yd = yd(xh, J), I can use ParametricPlot3D. But I failed when I faced this issue introduced above. Please help me. Thanks a lot for your support!