#45 Derivation

I knew that hysteretically damped rotor dynamic models were inherently nonlinear. Furthermore, I knew that such nonlinearities manifest themselves in the form of the absolute values of the cross-coupled terms. It was also clear to me that any eigenvalues extracted from a stability analysis of such a system would indicate the existence of a center manifold. Such results are, of course, inconclusive for a nonlinear system.

And so I decided to fit the nonlinearities with multivariate polynomials. This, I assured myself, would leave me with more manageable nonlinearities. I could simply normalize the new system and extract eigenvalues that would yield more conclusive results! If I could just free myself from this straightjacket, I could use my fingernails to etch the initial calculations into the walls.