I want to plot my eigenvector against r and theta, but I don't know how?

syms S r a theta
sigma_rr = (S/2)*(1-(a/r)^2)+(S/2)*(1-4*((a/r)^2)+3*(a/r)^4)*cos(2*theta)
sigma_00 = (S/2)*(1+(a/2)^2)-(S/2)*(1+3*(a/3)^4)*cos(2*theta)
sigma_0r = -(S/2)*(1+(2*(a/r)^2)-3*(a/r)^4)*sin(2*theta)


A= [sigma_rr, sigma_0r ; sigma_0r, sigma_00]

B= [cos(theta), sin(theta) ; -sin(theta), cos(theta)]

C=transpose(B)

D = C*B*A
e= eig(D)

[V,E]= eig(D)

plotmatrix(A)

Answer 1

[Ashutosh Singh Baghel]

Hi Friso,

I understand that you wish to plot the symbolic equations related to 'e'(eigenvector) against 'r' and 'theta'.

Please refer to the following workaround.

S = 5;          %Define S;
a = 5;          %Define a;

syms r theta

sigma_rr = (S/2)*(1-(a/r)^2)+(S/2)*(1-4*((a/r)^2)+3*(a/r)^4)*cos(2*theta);
sigma_00 = (S/2)*(1+(a/2)^2)-(S/2)*(1+3*(a/3)^4)*cos(2*theta);
sigma_0r = -(S/2)*(1+(2*(a/r)^2)-3*(a/r)^4)*sin(2*theta);

A = [sigma_rr, sigma_0r ; sigma_0r, sigma_00];
B = [cos(theta), sin(theta) ; -sin(theta), cos(theta)];
C = transpose(B);
D = C*B*A;

e = eig(D);

[V,E] = eig(D);

count = 0;
for i = [1 2]
    subplot(2,1,i);
    ezplot(e(i,1),[-10,10],[-2*pi,2*pi]);
end

Please feel free to refer to the documentation to the 'ezplot' function in MATLAB Documentation.