A specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures, ranging from jet engines and steam turbines to auto engines and computer disk storage. At its most basic level, rotordynamics is concerned with one or more mechanical structures (rotors) rotating around a single axis that are supported by bearings and influenced by internal phenomena. Rotordynamics is an indispensable tool for designing and troubleshooting industrial turbomachinery, such as pumps and compressors, gas and steam turbines, turbogenerators and turboexpanders, turbochargers, auxiliary power units, etc. The rotordynamics of turbomachinery encompasses the structural analysis of rotors (shafts and disks) and the design of fluid-film bearings and seals that determine the best dynamic performance given the required operating conditions. This best performance is denoted by well-characterized natural frequencies, and critical speeds, with amplitudes of synchronous dynamic response within required standards and demonstrated absence of subsynchronous vibration instabilities.