Lie Series Application to the Identification of a Multibody Mechanical System

A direct method of system identification and parameters monitoring is introduced for a general class of non-linear systems. The only requirement is that the system characteristics must be modeled by analytic or sufficiently smooth functions of the state variables, including the time parameter. The approach is based on the Lie operator representations and the corresponding Lie series solutions. This kind of solutions can be obtained for a general class of non-linear systems in the form of analytical power series including the system parameters. Despite of the local characterization of such solutions, the corresponding information carried by the solutions appears to be Sufficiently complete and provides precise estimates of the system parameters. In this paper a simple application is proposed. It is mainly addressed to identify the parameters of a mechanical system composed of a pendulum Jointed to a sliding mass. In this application a set of numerical results obtained by Integrating the motion equations has been used. Then, a numerical procedure has been developed in order to minimize the difference between numerical and approximating solution, at last obtained by using Lie series. Recently this methodology has been extended to differential systems with an unlimited number of equations and this allows one to treat non-linear partial differential equations arising from evolutionary or delayed problems [2,3]