How can plot 1D manifold in 3d space

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M
M 2022-6-21
回答： Torsten 2022-6-21
Hi, I have to plot a 1D manifold based on the equations below, x=[0,0.3], y=[0,1], z=[0,0.5]
other related equations are:
The 1D manifold in 3D space should be something like the red curve in the figure below:
For the convenience, the code of equations are:
g=(0:05).^4./z+(0:05).^4;
x=g;
p=0.255.*(z.^2./z.^2+(0.055).^2);
m1=0.15.^2./(p.^2+0.15.^2);
m2=z.^4./z.^4+0.1.^4;
m3=p.^2./p.^2+0.15.^2;
b=m2.*m3.*x;
a=m1.*(1-m2.*g);
f=1./1+0.4.*(1+a./b);
Thanks in advance for any help.
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M
M 2022-6-21
Sure, thanks again, I will check it and if it works I will accept your answer
M
M 2022-6-21
编辑：M 2022-6-21
@Torsten ,my problem is almost solved with your code, but because your answer is in the comment, I can't accept it as the best answer, so please write it as an answer if you like, then it would be chosen as the accepted answer, thanks.

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采纳的回答

Torsten
Torsten 2022-6-21
Ran in:
syms x y z
p=0.255*z.^2./(z.^2+(0.055)^2);
m1=0.15^2./(p.^2+0.15^2);
m2=z.^4./(z.^4+0.1^4);
m3=p.^2/(p.^2+0.15^2);
g = 0.05^4./(z+0.05^4);
a = m1.*(1-m2.*g);
b = m2.*m3.*x;
f = 1./(1+0.4*(1+a./b));
u = 0.18*f.*(5.5*y-6.5*z)-0.002*z.^2./(0.01+z.^2);
v = x - 0.05^4./(z+0.05^4) ;
u = subs(u,x,g);
Y = solve(u==0,y)
Y = 
Y = matlabFunction(Y);
z = 0.1:0.1:1;
y = Y(z);
x = 0.05^4./(z+0.05^4);
plot3(x,y,z)

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