De-orbiting and re-entry analysis with generalised intrusive polynomial expansions

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

3 Citations (Scopus)

Abstract

Generalised Intrusive Polynomial Expansion (GIPE) is a novel method for the propagation of multidimensional compact sets through dynamical systems. It generalises the more widely-known Taylor Differential Algebra in that it allows the use of generic polynomial representations of a multi-dimensional set. In particular the paper proposes the use of truncated Tchebycheff series. Unlike Taylor expansions, that are not generally convergent, Tchebycheff expansions provide fast uniform convergence with relaxed continuity and smoothness requirements, guaranteeing near-minimax approximation. This methodology has proven to be competitive for uncertainty propagation in orbital dynamics, especially when dealing with a large number of uncertain variables. Moreover, it provides the user with a complete polynomial representation of the uncertain region at any point of the propagation, allowing remarkable gain of insight into the underlying properties of the uncertain dynamics. The paper presents the application of the GIPE approach to the end-of-life analysis of Low Earth Orbit satellites, with special emphasis on the case of the de-orbiting and re-entry of GOCE and the de-orbiting of objects with high area to mass ratio. The effect of various sources of uncertainty on the end-of-life dynamics is thus analysed, such as the drag model or the accuracy of the initial orbit determination.

LanguageEnglish
Title of host publication67th International Astronautical Congress
Place of PublicationParis
Publication statusPublished - 26 Sep 2016
Event67th International Astronautical Congress - Expo Guadalajara, Guadalajara, Mexico
Duration: 26 Sep 201630 Sep 2016
Conference number: 67
https://www.iac2016.org

Publication series

NameProceedings of the International Astronautical Congress, IAC
PublisherInternational Astronautical Federation
ISSN (Print)0074-1795

Conference

Conference67th International Astronautical Congress
Abbreviated titleIAC
CountryMexico
CityGuadalajara
Period26/09/1630/09/16
Internet address

Fingerprint

GOCE
reentry
orbit determination
Reentry
drag
polynomials
Polynomials
expansion
methodology
propagation
Orbits
differential algebra
low Earth orbits
continuity
mass ratios
dynamical systems
Algebra
Drag
Dynamical systems
Earth (planet)

Keywords

  • re-entry analysis
  • generalised intrusive polynomial expansion
  • Taylor Differential Algebra
  • multidimensional compact sets
  • Tchebycheff series
  • end-of-life analysis
  • low-Earth orbit satellites
  • de-orbiting

Cite this

Absil, C. O., Serra, R., Riccardi, A., & Vasile, M. (2016). De-orbiting and re-entry analysis with generalised intrusive polynomial expansions. In 67th International Astronautical Congress (Proceedings of the International Astronautical Congress, IAC). Paris.
Absil, Carlos Ortega ; Serra, Romain ; Riccardi, Annalisa ; Vasile, Massimiliano. / De-orbiting and re-entry analysis with generalised intrusive polynomial expansions. 67th International Astronautical Congress. Paris, 2016. (Proceedings of the International Astronautical Congress, IAC).
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abstract = "Generalised Intrusive Polynomial Expansion (GIPE) is a novel method for the propagation of multidimensional compact sets through dynamical systems. It generalises the more widely-known Taylor Differential Algebra in that it allows the use of generic polynomial representations of a multi-dimensional set. In particular the paper proposes the use of truncated Tchebycheff series. Unlike Taylor expansions, that are not generally convergent, Tchebycheff expansions provide fast uniform convergence with relaxed continuity and smoothness requirements, guaranteeing near-minimax approximation. This methodology has proven to be competitive for uncertainty propagation in orbital dynamics, especially when dealing with a large number of uncertain variables. Moreover, it provides the user with a complete polynomial representation of the uncertain region at any point of the propagation, allowing remarkable gain of insight into the underlying properties of the uncertain dynamics. The paper presents the application of the GIPE approach to the end-of-life analysis of Low Earth Orbit satellites, with special emphasis on the case of the de-orbiting and re-entry of GOCE and the de-orbiting of objects with high area to mass ratio. The effect of various sources of uncertainty on the end-of-life dynamics is thus analysed, such as the drag model or the accuracy of the initial orbit determination.",
keywords = "re-entry analysis, generalised intrusive polynomial expansion, Taylor Differential Algebra, multidimensional compact sets, Tchebycheff series, end-of-life analysis, low-Earth orbit satellites, de-orbiting",
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Absil, CO, Serra, R, Riccardi, A & Vasile, M 2016, De-orbiting and re-entry analysis with generalised intrusive polynomial expansions. in 67th International Astronautical Congress. Proceedings of the International Astronautical Congress, IAC, Paris, 67th International Astronautical Congress, Guadalajara, Mexico, 26/09/16.

De-orbiting and re-entry analysis with generalised intrusive polynomial expansions. / Absil, Carlos Ortega; Serra, Romain; Riccardi, Annalisa; Vasile, Massimiliano.

67th International Astronautical Congress. Paris, 2016. (Proceedings of the International Astronautical Congress, IAC).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

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T1 - De-orbiting and re-entry analysis with generalised intrusive polynomial expansions

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AU - Riccardi, Annalisa

AU - Vasile, Massimiliano

PY - 2016/9/26

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N2 - Generalised Intrusive Polynomial Expansion (GIPE) is a novel method for the propagation of multidimensional compact sets through dynamical systems. It generalises the more widely-known Taylor Differential Algebra in that it allows the use of generic polynomial representations of a multi-dimensional set. In particular the paper proposes the use of truncated Tchebycheff series. Unlike Taylor expansions, that are not generally convergent, Tchebycheff expansions provide fast uniform convergence with relaxed continuity and smoothness requirements, guaranteeing near-minimax approximation. This methodology has proven to be competitive for uncertainty propagation in orbital dynamics, especially when dealing with a large number of uncertain variables. Moreover, it provides the user with a complete polynomial representation of the uncertain region at any point of the propagation, allowing remarkable gain of insight into the underlying properties of the uncertain dynamics. The paper presents the application of the GIPE approach to the end-of-life analysis of Low Earth Orbit satellites, with special emphasis on the case of the de-orbiting and re-entry of GOCE and the de-orbiting of objects with high area to mass ratio. The effect of various sources of uncertainty on the end-of-life dynamics is thus analysed, such as the drag model or the accuracy of the initial orbit determination.

AB - Generalised Intrusive Polynomial Expansion (GIPE) is a novel method for the propagation of multidimensional compact sets through dynamical systems. It generalises the more widely-known Taylor Differential Algebra in that it allows the use of generic polynomial representations of a multi-dimensional set. In particular the paper proposes the use of truncated Tchebycheff series. Unlike Taylor expansions, that are not generally convergent, Tchebycheff expansions provide fast uniform convergence with relaxed continuity and smoothness requirements, guaranteeing near-minimax approximation. This methodology has proven to be competitive for uncertainty propagation in orbital dynamics, especially when dealing with a large number of uncertain variables. Moreover, it provides the user with a complete polynomial representation of the uncertain region at any point of the propagation, allowing remarkable gain of insight into the underlying properties of the uncertain dynamics. The paper presents the application of the GIPE approach to the end-of-life analysis of Low Earth Orbit satellites, with special emphasis on the case of the de-orbiting and re-entry of GOCE and the de-orbiting of objects with high area to mass ratio. The effect of various sources of uncertainty on the end-of-life dynamics is thus analysed, such as the drag model or the accuracy of the initial orbit determination.

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CY - Paris

ER -

Absil CO, Serra R, Riccardi A, Vasile M. De-orbiting and re-entry analysis with generalised intrusive polynomial expansions. In 67th International Astronautical Congress. Paris. 2016. (Proceedings of the International Astronautical Congress, IAC).