STABILITY OF SOME NONLINEAR SYSTEMS

Abstract : The stability of systems governed by x double dot + f(x) + q(x, x dot)x dot - phi(t) r(x) = S(x;t) is studied. Liapunov's Direct Method and a linearization approach have been used in the study of stability of the above system for phi(t) L sub 1 integrable, and periodic, respectively. In the former case a sufficiency region of stability is constructed through the use of a Liapunov function. In the latter case, which is investigated by means of a linearization process, a Hill equation is obtained, whose stability is studied by a method suggested by Malkin. Malkin's method is then modified to obtain, by use of a first approximation, the first stability region in parameter space. A second approximation is also worked out. When the approximations obtained herein for general periodic function are reduced to the special cases of the Mathieu equation and the Hill-3-term equation, the results compare very well with the available numerical results based on the exact solution of each of those equations. (Author)