### Abstract

A conservative time integration algorithm for rigid body rotations is presented in a purely algebraic form in terms of the four quaternions components and the four conjugate momentum variables via Hamilton’s equations. The introduction of an extended mass matrix leads to a symmetric set of eight state-space equations where constraints are embedded without explicit use of Lagrange multipliers. The algorithm is developed by forming a finite increment of the Hamiltonian, which defines the proper selection of increments and mean values that leads to conservation of energy and momentum. The accuracy and conservation properties are illustrated by examples.

Original language | English |
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Title of host publication | Proceedings of the 25th Nordic Seminar on Computational Mechanics |

Editors | K. Persson, J. Revstedt, G. Sandberg, M. Wallin |

Number of pages | 4 |

Publisher | Lund University Faculty of Engineering |

Publication date | 2012 |

ISBN (Print) | 978-91-7473-456-0 |

Publication status | Published - 2012 |

Event | NSCM25: 25th Nordic Seminar on Computational Mechanics - University of Lund, Lund, Sweden Duration: 25 Oct 2012 → 26 Oct 2012 |

### Conference

Conference | NSCM25 |
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Location | University of Lund |

Country | Sweden |

City | Lund |

Period | 25/10/2012 → 26/10/2012 |

### Keywords

- Finite rotations
- Quaternion parameters
- Conservative integration

## Cite this

Nielsen, M. B., & Krenk, S. (2012). A conservative quaternion-based time integration algorithm for rigid body rotations with implicit constraints. In K. Persson, J. Revstedt, G. Sandberg, & M. Wallin (Eds.),

*Proceedings of the 25th Nordic Seminar on Computational Mechanics*Lund University Faculty of Engineering.