In my mechanical vibrations class we studied the method to orthonormalize a set of differential equations by the mass matrix (principle coordinates). This is where you take the matrix of eigenvectors from the un-damped system and normalize it by the mass matrix.
Multiplying the mass matrix by the modal matrix gives:
X'MX = I
And multiplying the stiffness matrix by the modal matrix gives:
X'KX = W^2(ii)
Where W^2(ii) is the matrix of squared natural frequencies.
My question is: is it appropriate to try and orthonormalize the damping matrix in the same fashion?
X'CX = 2*zeta*omega(ii)
Should this transform the system's damping into principle coordinates?