<div class="section abstract"><div class="htmlview paragraph">Gyroscopic effects split circumferential traveling-wave resonances of rotating structures into forward and backward branches. This work first analyzes the splitting in the co-rotating (Lagrangian) frame to provide physical intuition for the evolution of the two branches with spin speed. A transformation to the inertial (Eulerian) frame is then derived, showing that the observed frequencies are shifted by a kinematic Dopple