### Abstract

Language | English |
---|---|

Pages | 40-49 |

Number of pages | 10 |

Journal | Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science |

Volume | 225 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1 Jan 2011 |

### Fingerprint

### Keywords

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

### Cite this

*Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science*,

*225*(1), 40-49. https://doi.org/10.1243/09544062JMES2473

}

*Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science*, vol. 225, no. 1, pp. 40-49. https://doi.org/10.1243/09544062JMES2473

**The implementation of an automated method for solution term-tracking as a basis for symbolic computational dynamics.** / Forehand, D.I.M.; Cartmell, M.P.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The implementation of an automated method for solution term-tracking as a basis for symbolic computational dynamics

AU - Forehand, D.I.M.

AU - Cartmell, M.P.

PY - 2011/1/1

Y1 - 2011/1/1

N2 - 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.

AB - 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.

KW - term tracking in symbolic computer algebra

KW - symbolic computational dynamics

KW - non-linear engineering dynamics

KW - perturbation methods

KW - multiple scales

UR - http://pic.sagepub.com/content/225/1/40.abstract

UR - https://www.scopus.com/inward/record.uri?eid=2-s2.0-79251498613&partnerID=40&md5=f2b03fa29858ba2e16b9fc579dfe3627

U2 - 10.1243/09544062JMES2473

DO - 10.1243/09544062JMES2473

M3 - Article

VL - 225

SP - 40

EP - 49

JO - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

T2 - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

JF - Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science

SN - 0954-4062

IS - 1

ER -