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Celestial Mechanics and Dynamical Astronomy

, Volume 122, Issue 3, pp 239–261 | Cite as

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

  • Alexander Wittig
  • Pierluigi Di Lizia
  • Roberto Armellin
  • Kyoko Makino
  • Franco Bernelli-Zazzera
  • Martin Berz
Original Article

Abstract

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.

Keywords

Differential algebra Automatic domain splitting Uncertainty propagation Apophis resonant return 

Notes

Acknowledgments

A. Wittig gratefully acknowledges the support received by the EU Marie Curie fellowship from the initial training network PITN-GA 2011-289240 (AstroNet-II).

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Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Alexander Wittig
    • 1
  • Pierluigi Di Lizia
    • 1
  • Roberto Armellin
    • 2
  • Kyoko Makino
    • 3
  • Franco Bernelli-Zazzera
    • 1
  • Martin Berz
    • 3
  1. 1.Department of Aerospace Science and TechnologyPolitecnico di MilanoMilanItaly
  2. 2.Aeronautics, Astronautics and Computational Engineering UnitUniversity of SouthamptonSouthamptonUK
  3. 3.Department of Physics and AstronomyMichigan State UniversityEast LansingUSA

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