Perturbation methods for slightly damped gyroscopic systems

The perturbation theory was initially developed as an efficient means of solving the eigenvalue problem associated with linear gyroscopic systems for which the damping and/or circulatory effects are sufficiently small that they can be regarded as perturbations. The perturbation theory is applied to an example of such a system. One interesting aspect of this example is that for one of the combinations of parameters, it exhibits both divergence and flutter instability, simultaneously. Other numerical examples are given.