The implementation of an automated method for solution term-tracking as a basis for symbolic computational dynamics

Abstract

This article proposes that additional mathematical information, inherent and implicit within mathematical models of physical dynamic systems, can be extracted and visualized in a physically meaningful and useful manner as an adjunct to standard analytical modelling and solution. A conceptual methodology is given for a process of term-tracking within ordinary differential equation (ODE) models and solutions for engineering dynamics problems, and for a visualization based on a powerful new Mathematica implementation of the standard Tooltip graphical user interface facility. It is shown that the method is logical, generic, and unambiguous in its application, and that a useful visualization tool can be devised, and structured in such a way that the user can be given as much or as little information as is required to assimilate the problem to hand. The article shows by means of examples of code written expressly for the purpose that a term-tracking and visualization methodology can be constructed in a computationally effective manner within Mathematica and applied to a semi-automated variant of the method of multiple scales. It is implicitly obvious that this approach can therefore be applied to almost any algorithmic symbolic solution method, and therefore there could be physical applications which are potentially well beyond the chosen domain of non-linear engineering dynamics.

Keywords

term-tracking in symbolic computer algebra symbolic computational dynamics non-linear engineering dynamics perturbation methods multiple scales

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