This paper presents a new modal analysis that permits the derivation of closed-form response of linear gyroscopic systems in a manner similar to that in which the classical modal analysis permits the derivation of the response of natural elastic systems. The method has important implications in the dynamics and control of rotating systems. As an illustration, the response of a spinning rigid body containing flexible parts is derived. This represents the first time that the response of a linear gyroscopic system to external excitation is derived in closed form.

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