Nonautonomous Second-order Systems Research Articles

A generalized Bessel equation and synthesis of second-order non-autonomous systems

A parametric constraint for a general, second-order, linear, non-autonomous system to possess responses expressible in terms of the well-known Bessel functions is presented. In effect, this paper develops a process of synthesis (of systems with a Bessel typo of responses) which can be programmed using algebraic languages to obtain a practical tool of study.

Amplitude bounds for second-order nonautonomous systems

A method is described for obtaining bounds on the response of 2nd-order nonautonomous systems. The method, which is an extension of the tracking-function method, obtains a closed bounded region in the state plane to which the system trajectories are confined. Originally conceived as a graphical procedure applicable only to autonomous systems, the method is well suited to numerical computation, which both increases its power and facilitates its application. Several examples illustrate the method and show it to be of wider applicability than previous methods.