Using Symbolic Computational Dynamics as an Aid to Design

Abstract

The topic of Symbolic Computational Dynamics, as presented here, has been motivated by the utility of approximate analytical solutions for reduced order models, and the power of computers to cope with the challenges of both problem scale and automation. Application has traditionally been limited by the algebra needed for problems of more than a few coupled coordinates, making such problems excellent candidates for automation through symbolic computation. But there is a lot of useful information that is naturally lost when doing this, due to the on-going processes of algebraic simplification, the different mathematical-physical processes behind the small parameter, and defining relative strengths of physically based terms. We offer a novel symbolic computational process that applies a semi-automated asymptotic method for solution that also retains all information, leading to a first generation approach to the global visualisation of problems in dynamics.