### Abstract

The paper presents the use of positive polynomials, in particular Bernstein polynomials, to represent families of probability distributions in orbital dynamics. The uncertainty in model parameters and initial conditions is modeled with p-boxes to account for imprecision and lack of knowledge. The resulting uncertainty in the quantity of interest is estimated by representing the upper and lower expectations with positive polynomials with interval coefficients. The impact probability of an asteroid subject to a partially known Yarkovsky effect is used as an illustrative example.

Language | English |
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Title of host publication | Stardust Final Conference |

Subtitle of host publication | Advances in Asteroids and Space Debris Engineering and Science |

Editors | Massimiliano Vasile, Edmondo Minisci, Leopold Summerer, Peter McGinty |

Place of Publication | Cham |

Publisher | Springer |

Pages | 99-107 |

Number of pages | 9 |

ISBN (Print) | 9783319699554, 9783319699561 |

DOIs | |

Publication status | E-pub ahead of print - 11 Feb 2018 |

Event | Stardust Final Conference on Asteroids and Space Debris - ESA-ESTEC, Netherlands Duration: 31 Oct 2016 → 3 Nov 2016 https://www.stardust2013.eu/Training/Conferences/StardustFinalConference/tabid/5484/Default.aspx |

### Publication series

Name | Astrophysics and Space Science Proceedings |
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Publisher | Springer |

Volume | 52 |

ISSN (Print) | 1570-6591 |

### Conference

Conference | Stardust Final Conference on Asteroids and Space Debris |
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Country | Netherlands |

Period | 31/10/16 → 3/11/16 |

Internet address |

### Fingerprint

### Keywords

- positive polynomials
- Bernstein polynomials
- orbital dynamics
- impact probability
- Yarkovsky effect

### Cite this

*Stardust Final Conference: Advances in Asteroids and Space Debris Engineering and Science*(pp. 99-107). (Astrophysics and Space Science Proceedings; Vol. 52). Cham: Springer. https://doi.org/10.1007/978-3-319-69956-1_6

}

*Stardust Final Conference: Advances in Asteroids and Space Debris Engineering and Science.*Astrophysics and Space Science Proceedings, vol. 52, Springer, Cham, pp. 99-107, Stardust Final Conference on Asteroids and Space Debris, Netherlands, 31/10/16. https://doi.org/10.1007/978-3-319-69956-1_6

**On the use of positive polynomials for the estimation of upper and lower expectations in orbital dynamics.** / Vasile, Massimiliano; Tardioli, Chiara.

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

TY - GEN

T1 - On the use of positive polynomials for the estimation of upper and lower expectations in orbital dynamics

AU - Vasile, Massimiliano

AU - Tardioli, Chiara

PY - 2018/2/11

Y1 - 2018/2/11

N2 - The paper presents the use of positive polynomials, in particular Bernstein polynomials, to represent families of probability distributions in orbital dynamics. The uncertainty in model parameters and initial conditions is modeled with p-boxes to account for imprecision and lack of knowledge. The resulting uncertainty in the quantity of interest is estimated by representing the upper and lower expectations with positive polynomials with interval coefficients. The impact probability of an asteroid subject to a partially known Yarkovsky effect is used as an illustrative example.

AB - The paper presents the use of positive polynomials, in particular Bernstein polynomials, to represent families of probability distributions in orbital dynamics. The uncertainty in model parameters and initial conditions is modeled with p-boxes to account for imprecision and lack of knowledge. The resulting uncertainty in the quantity of interest is estimated by representing the upper and lower expectations with positive polynomials with interval coefficients. The impact probability of an asteroid subject to a partially known Yarkovsky effect is used as an illustrative example.

KW - positive polynomials

KW - Bernstein polynomials

KW - orbital dynamics

KW - impact probability

KW - Yarkovsky effect

UR - http://www.scopus.com/inward/record.url?scp=85041966848&partnerID=8YFLogxK

UR - https://link.springer.com/book/10.1007/978-3-319-69956-1

UR - https://www.stardust2013.eu/Training/Conferences/StardustFinalConference/tabid/5484/Default.aspx

U2 - 10.1007/978-3-319-69956-1_6

DO - 10.1007/978-3-319-69956-1_6

M3 - Conference contribution book

SN - 9783319699554

SN - 9783319699561

T3 - Astrophysics and Space Science Proceedings

SP - 99

EP - 107

BT - Stardust Final Conference

A2 - Vasile, Massimiliano

A2 - Minisci, Edmondo

A2 - Summerer, Leopold

A2 - McGinty, Peter

PB - Springer

CY - Cham

ER -