Stability of linear gyroscopic systems: A review

Following an introductory section with important definitions and concepts, Section 2 concerns algebraic results for undamped time-invariant linear systems. In Section 3 we consider the effects of adding viscous damping to the preceding models. This includes discussion of parameter-dependent systems and the so-called Thomson, Tait, Chetaev circle of ideas. Proofs are provided if they are not readily accessible in the literature. There are appendices containing minimal related information on controllability and perturbation theory.