### Abstract

Computational efficiency of solving the dynamics of highly oscillatory systems is an important issue due to the requirement of small step size of explicit numerical integration algorithms. A system is considered to have an oscillatory solution if it contains a fast solution that varies regularly about a slow solution. This paper investigates the use of the so-called Local Linearization Method (LLM) in the integration of multibody equations of motion that exhibit oscillatory behavior. The LLM is an exponential method that is based on the piecewise linear approximation of the equations through a firstorder Taylor expansion at each time step, where the solution at the next time step is determined by the analytic solution of the approximated linear system. In this paper the LLM is applied to simple examples. The results show that the LLM can improve computational efficiency, without jeopardizing the accuracy, when the multibody system is highly oscillatory.

Original language | English (US) |
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Title of host publication | Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2013 |

Pages | 613-622 |

Number of pages | 10 |

State | Published - Dec 1 2013 |

Event | ECCOMAS Thematic Conference on Multibody Dynamics 2013 - Zagreb, Croatia Duration: Jul 1 2013 → Jul 4 2013 |

### Publication series

Name | Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2013 |
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### Other

Other | ECCOMAS Thematic Conference on Multibody Dynamics 2013 |
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Country | Croatia |

City | Zagreb |

Period | 7/1/13 → 7/4/13 |

### Keywords

- Highly oscillatory system
- Local Linearization Method
- Local error estimation
- Numerical integration

### ASJC Scopus subject areas

- Computer Science (miscellaneous)

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## Cite this

*Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2013*(pp. 613-622). (Proceedings of the ECCOMAS Thematic Conference on Multibody Dynamics 2013).