An Algebraic Method for Analyzing Open-Loop Dynamic Systems

This paper reports on the results of combining the Maple packages Dynaflex and RifSimp. The Dynaflex package has been developed to generate the governing dynamical equations for mechanical systems; the RifSimp package has been developed for the symbolic analysis of differential equations. We show that the output equations from Dynaflex can be converted into a form which can be analyzed by RifSimp. Of particular interest is the ability of RifSimp to split a set of differential equations into different cases; each case corresponds to a different set of assumptions, and under some sets of assumptions there are significant simplifications. In order to allow RifSimp to conduct its analysis, the governing equations must be converted from trigonometric form into a polynomial form. After this is done, RifSimp can analyze the system and present its results either graphically, or in list form. The mechanical systems considered are restricted to open-loop systems, because at present, closed-loop systems require too much computation by RifSimp to permit analysis.