A modeling via Hamilton's law with application to a model following resembling technique

Abstract

As a result of direct application of Hamilton's law of varying action on the treatment of mechanical systems, solving both dynamic and control problems is done using algebraic equations only; no differential equations are needed. In these techniques both the dynamic response and control forces are assumed to be a truncated power series. The target was only to solve the concerned problem. Using the coefficients of the above-mentioned polynomials in the vector form, an input-output model for the mechanical system to follow a specified path, while it is perturbed out of that path, is introduced herein. The modeling uses only algebraic equations. In this work, a model following resembling technique is demonstrated as a useful application of this modeling way. That is to get the required input forcing function to obligate the mechanical system to behave like a reference system when it is shifted away from the specified path.