Unusual gyroscopic system eigenvalue behavior in high-speed planetary gears

This study demonstrates unusual gyroscopic system eigenvalue behavior observed in a lumped-parameter planetary gear model. While the model has been used for dynamic analyses in industrial applications, the focus is on the eigenvalue phenomena that occur at especially high speeds rather than practical planetary gear behavior. The behaviors include calculation of exact trajectories across critical speeds, uncommon stability features near degenerate critical speeds, and unique stability transitions. These eigenvalue behaviors are not evident in the vast literature on gyroscopic systems.