Abstract: This paper gives a dynamic decoupling approach for the analysis of large scale non classically damped system, in which the complex number computations were completely avoided not only in solving for the eigenvalue problem but also in the calculation of the dynamic response.The analytical approach for undamped gyroscopic system, non classicaly damped system, including the damped gyroscopic system were unified. Very interesting and useful theoretical results, practical algorithms were obtained which is appl...