Interpretation of Floquet Eigenvalues and Eigenvectors for Periodic Systems

The application of Floquet analysis to rotorcraft has demonstrated that there is often misunderstanding as to how to interpret the integer-multiple arbitrariness in the imaginary part of the characteristic exponents of the system (i. e., in the frequency). Although some papers have offered various methodologies for choosing the "correct" frequency (such as choice of the strongest harmonic in the periodic eigenvector), confusion still persist and none of the proposed methods completely solves the difficulty. The purpose of this present paper is to (1) offer a history of analysis of periodic systems with respect to the treatment of the integer multiples, (2) propose a practical tool for fundamental insight into system frequencies, and (3) show demonstratively for simple cases why no single integer can adequately describe system dynamics. It is hoped that this approach will provide clarity to a problem that, although long understood in principle, still leads to confusion in published papers.