Propagation of large uncertainty sets in orbital dynamics by automatic domain splitting

  1. Wittig, A. 2
  2. Di Lizia, P. 2
  3. Armellin, R. 1
  4. Makino, K. 3
  5. Bernelli-Zazzera, F. 2
  6. Berz, M. 3
  1. 1 University of Southampton
    info

    University of Southampton

    Southampton, Reino Unido

    ROR https://ror.org/01ryk1543

  2. 2 Polytechnic University of Milan
    info

    Polytechnic University of Milan

    Milán, Italia

    ROR https://ror.org/01nffqt88

  3. 3 Michigan State University
    info

    Michigan State University

    East Lansing, Estados Unidos

    ROR https://ror.org/05hs6h993

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Zeitschrift:
Celestial mechanics and dynamical astronomy

ISSN: 0923-2958

Datum der Publikation: 2015

Ausgabe: 122

Nummer: 3

Seiten: 239-261

Art: Artikel

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DOI: 10.1007/S10569-015-9618-3 SCOPUS: 2-s2.0-84930384219 GOOGLE SCHOLAR

Andere Publikationen in: Celestial mechanics and dynamical astronomy

Institutionelles Repository: lockOpen Access Editor

Zusammenfassung

Current approaches to uncertainty propagation in astrodynamics mainly refer to linearized models or Monte Carlo simulations. Naive linear methods fail in nonlinear dynamics, whereas Monte Carlo simulations tend to be computationally intensive. Differential algebra has already proven to be an efficient compromise by replacing thousands of pointwise integrations of Monte Carlo runs with the fast evaluation of the arbitrary order Taylor expansion of the flow of the dynamics. However, the current implementation of the DA-based high-order uncertainty propagator fails when the non-linearities of the dynamics prohibit good convergence of the Taylor expansion in one or more directions. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial expansion of the current state is split into two polynomials whenever its truncation error reaches a predefined threshold. The resulting set of polynomials accurately tracks uncertainties, even in highly nonlinear dynamics. The method is tested on the propagation of (99942) Apophis post-encounter motion. © 2015, Springer Science+Business Media Dordrecht.