Dear Martin,
I generally agree that the eigenvalues of a linear second-order system form complex conjugate pairs. This is summarized a bit in my post dated Aug 20, 2020 in the following forum topic: BeamDyn: add point masses and show eigenfrequencies - #7 by Jason.Jonkman. Of course, you won’t have the complex eigenvalue pair if you have rigid-body modes (whereby omega_n = 0) or an overly damped system (ABS(zeta) >= 1), where the imaginary part is zero.
And I also agree that an OpenFAST linearization analysis will produce a linear model that should generate such eigenvalues. I gather you are seeing that for the surge and sway modes, but not other modes? Can you clarify what you are seeing?
Note that if HydroDyn states are included in the OpenFAST linearization, then these states don’t include second time derivatives. This is explained a bit in our DeepWind 2019 paper: iopscience.iop.org/article/10.1 … 012022/pdf.
Best regards,