You are absolutely right. I was a bit general with my conclusion there. The eigenvectors for an isotropic solid are valid for all θ when normalized as you suggested. However, looking back at the original eigenvectors:
\begin{eqnarray*}
\mathbf{\hat{u}}_1 &=& \begin{Bmatrix}
0\\
1 \\
0...
Thank you Darwin123 for taking the time to write such a thorough answer.
I should maybe have been more precise in that I am working with elastic waves (stress waves) in solid media. I know many of the same principles apply to optics as to elasticity, but there are some differences in the...
You are right; I do not need Maple to solve the problem. Nevertheless, it is convenient if I want to change the stiffness coefficient values or if I want to insert different values for θ. Also, taking the limit of the mentioned eigenvectors is not straight forward by hand (L'Hopital's rule...
If I first insert θ=0.1 and then insert θ=0.001, I see that the norm of the eigenvector u3 increases rapidly. So I have all reason to suspect that 'undefined' in this case means 'infinity'.
I know that for θ=0, for example, the eigenvectors should be u1=[0, 1, 0], u2=[0, 0, 1] and u3=[1, 0...
Hey guys! (I am not sure if I should post this thread in Physics or Mathematics)
I have had some issues with developing expressions for the polarizations (material displacement) of waves propagating in anisotropic media. To bring you guys up to speed I have to start a few steps before the...