### Abstract

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.

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

*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.

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*Astrodynamics 2015: Proceedings of the AAS/AIAA Astrodynamics Specialist Conference held August 9–13, 2015, Vail, Colorado, U.S.A..*Advances in Astrnautical Sciences, vol. 156, San Diego, California, pp. 707-722, AAS/AIAA Astrodynamics Specialist Conference 2015, Vail, United States, 9/08/15.

**An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra.** / Riccardi, Annalisa; Tardioli, Chiara; Vasile, Massimiliano.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

TY - GEN

T1 - An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra

AU - Riccardi, Annalisa

AU - Tardioli, Chiara

AU - Vasile, Massimiliano

N1 - This paper was originally presented at the AAS/AIAA Astrodynamics Specialist Conference held August 9-13, 2015, Vail, Colorado, U.S.A., and was originally published in the American Astronautical Society (AAS) publication Astrodynamics 2015, edited by Manoranjan Majji, James D. Turner, Geoff G. Wawrzyniak and William Todd Cerven, American Astronautical Society (AAS) Advances in the Astronautical Sciences, Volume 156, 2016, pp. 4205-4220 (Copyright © 2016 by American Astronautical Society Publications Office, P.O. Box 28130, San Diego, CA 92198, U.S.A.; Web Site: http://www.univelt.com

PY - 2015/8/13

Y1 - 2015/8/13

N2 - 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.

AB - 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.

KW - algebra

KW - uncertainty analysis

KW - mechanics

KW - astrophysics

KW - approximation accuracy

KW - uniform convergence

KW - uncertainty propagation

KW - series expansion

KW - polynomial algebra

KW - orbital mechanics

KW - non-intrusive

KW - model uncertainties

UR - http://www.scopus.com/inward/record.url?scp=85007308349&partnerID=8YFLogxK

UR - http://www.space-flight.org/docs/2015_astro/2015_astro.html

UR - http://www.univelt.com/book=5315

M3 - Conference contribution book

SN - 9780877036296

T3 - Advances in Astrnautical Sciences

SP - 707

EP - 722

BT - Astrodynamics 2015

A2 - Turner, J. D.

A2 - Wawrzyniak, G. G.

A2 - Cerven , W. T.

A2 - Majji, M.

CY - San Diego, California

ER -