Abstract
Symbolic computational dynamic solvers are currently under development in order to provide new and powerful tools for modelling nonlinear dynamical systems. Such solvers consist of two parts; the core solver, which comprises an approximate analytical method based on perturbation, averaging, or harmonic balance, and a specialised term-tracker. A term-tracking approach has been introduced to provide a powerful new feature into computational approximate analytical solutions by highlighting the many mathematical connections that exist, but which are invariably lost through processing, between the physical model of the system, the solution procedure itself, and the final result which is usually expressed in equation form. This is achieved by a highly robust process of term-tracking, recording, and identification of all the symbolic mathematical information within the problem. In this paper, the novel source and evolution encoding method is introduced for the first time and an implementation in Mathematica is described through the development of a specialised algorithm.
| Original language | English |
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| Journal | Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science |
| Early online date | 5 Nov 2017 |
| DOIs | |
| Publication status | E-pub ahead of print - 5 Nov 2017 |
Keywords
- symbolic computational dynamics
- term-tracking methods
- source and evolution encoding method
- multiple scales method
- approximate analytical methods
- nonlinear dynamics
- Mathematica
