### Abstract

The paper presents an intrusive approach to propagate uncertainty in orbital mechanics. The approach is based on an expansion of the uncertain quantities in Tchebicheff series and a propagation through the dynamics using a generalised polynomial algebra.

Tchebicheff series expansions offer a fast uniform convergence with relaxed continuity and smothness requirements. The paper details the proposed approach and illustrates its applicability through a set of test cases considering both parameter and model uncertainties. This novel intrusive technique is then comapred against its non-intrusive counterpart in terms of approximation accuracy and computational cost.

Tchebicheff series expansions offer a fast uniform convergence with relaxed continuity and smothness requirements. The paper details the proposed approach and illustrates its applicability through a set of test cases considering both parameter and model uncertainties. This novel intrusive technique is then comapred against its non-intrusive counterpart in terms of approximation accuracy and computational cost.

Original language | English |
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Title of host publication | Astrodynamics 2015 |

Subtitle of host publication | Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A. |

Editors | J. D. Turner, G. G. Wawrzyniak, W. T. Cerven , M. Majji |

Place of Publication | San Diego, California |

Pages | 707-722 |

Number of pages | 16 |

Publication status | Published - 13 Aug 2015 |

Event | AAS/AIAA Astrodynamics Specialist Conference 2015 - Colorado, Vail, United States Duration: 9 Aug 2015 → 13 Aug 2015 |

### Publication series

Name | Advances in Astrnautical Sciences |
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Publisher | American Astronautical Society |

Volume | 156 |

ISSN (Print) | 0065-3438 |

### Conference

Conference | AAS/AIAA Astrodynamics Specialist Conference 2015 |
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Country | United States |

City | Vail |

Period | 9/08/15 → 13/08/15 |

### Fingerprint

### Keywords

- algebra
- uncertainty analysis
- mechanics
- astrophysics
- approximation accuracy
- uniform convergence
- uncertainty propagation
- series expansion
- polynomial algebra
- orbital mechanics
- non-intrusive
- model uncertainties

### Cite this

Riccardi, A., Tardioli, C., & Vasile, M. (2015). An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra. In J. D. Turner, G. G. Wawrzyniak, W. T. Cerven , & M. Majji (Eds.),

*Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A.*(pp. 707-722). (Advances in Astrnautical Sciences; Vol. 156). San Diego, California.