Search

A method is described for the determination of the regions of the parameter space corresponding to stability and instability of the null solution of a restricted system of linear, periodic-coefficient ordinary homogeneous differential equations. The method is applicable to equations which represent the motion of a completely damped mechanical system. For such systems, there can be no periodic or almost-periodic solutions within the region of the parameter space corresponding to stable null solutions. Accordingly, by establishing those parameter values for which almost-periodic solutions are possible, one can determine the boundaries of the regions in the parameter space corresponding to stable solutions. This is accomplished by substituting an almost-periodic solution as the product of a specific periodic function and a Fourier series, obtaining by numerical search those parameter values which guarantee the existence of such a solution by the vanishing of a suitable approximation of a determinant of infinite size. This method is applied to a current problem in space vehicle dynamics, and comparison is made with a numerical implementation of Floquet theory.