Many mechanical systems have the mathematical model as Mx¨ + Dx˙ + Kx=0. For this mathematical model of systems T. K. Caughey, M. E. J. Kelly, and D. W. Nicholson studied its uncoupling properties and gave out the sufficient and necessary conditions for the complete decomposition of the system. In this paper the author made an effort to develop the results obtained before. The concept of decomposition degree of mechanical system is given and the sufficient and necessary conditions for determining a system to be locally decomposable are obtained. In the last section a system is given which is not completely decomposable but locally decomposable.

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