Uncoupling of Linear Multi-degree of Freedom Damped Gyroscopic Potential Systems

This paper deals with the uncoupling of linear damped multi-degree of freedom gyroscopic potential systems in which the damping is taken to have a specifically chosen form. Necessary and sufficient conditions are obtained that guarantee the uncoupling of such damped systems into independent subsystems with at most two-degrees-of-freedom. Along with several other results, it is shown that when the potential (stiffness) matrix of the damped system has distinct eigenvalues—a situation commonly found in civil, mechanical, and aerospace engineering, as well as in Nature—the damping matrix must have this specifically chosen form for any such multi-degree-of-freedom system to be capable of being uncoupled.