PERTURBATION METHOD FOR THE FLOQUET EIGENVALUES AND STABILITY BOUNDARY OF PERIODIC LINEAR-SYSTEMS

A multiple parameter perturbation method is developed to determine the Floquet eigenvalues and stability boundary of a linear discrete syste m that is described by a system of ordinary differential equations wit h periodic coefficients. In the method, the state of the system is det ermined by solving a number of decoupled problems and, as a result, im plementation of the method is computationally efficient even when the dimension of the system is large. The method is first applied to Mathi eu's equation in order to illustrate its application to a relatively s traightforward, standard problem. It is then applied to the torsional analysis of a boat's drive train to show application to a large scale system of some practical importance.