| Abstract: | A certainclass of sigularly-perturbed systems which have a variety of m-dimensional stationary positions is considered. When a small parameter disappears, the system also has an m-dimensional manifold of stationary positions and, therefore, the corresponding characteristic equation has m zero roots. The conditions under which the solution of a stability problem reduces to the same problem for a degenerate system are defined. As an application in practice gyroscopic stabilizing systems (the critical case corresponds to such systems) with elastic elements of high stiffness are discussed. The conditions under which the solution of the problem of the stability of steady motion follows from the solution of this problem for an ideal system (with absolutely rigid elements) are obtained. The problem of the closeness of the corresponding solutions of the complete and a simplified system of differential equations over an infinite time interval is discussed. |
