This paper gives a dynamic decoupling approach for the analysis of lar
ge scale non-classically damped system, in which the complex variable
computations were completely avoided not only in solving for the eigen
value problem but also in the calculation of the dynamic response. The
analytical approaches for undamped gyroscopic system, non-classically
damped system, including the damped gyroscopic system were unified. V
ery interesting and useful theoretical results, practical algorithms w
ere obtained which are applicable to both non-defective and defective
systems.