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Long term nonlinear propagation of uncertainties in perturbed geocentric dynamics using automatic domain splitting

Long term nonlinear propagation of uncertainties in perturbed geocentric dynamics using automatic domain splitting
Long term nonlinear propagation of uncertainties in perturbed geocentric dynamics using automatic domain splitting

Current approaches to uncertainty propagation in astrodynamics mainly refer to linearize 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 in highly nonlinear dynamics or long term propagation. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial of the current state is split in two polynomials when its accuracy reaches a given threshold. The resulting polynomials accurately track uncertainties, even in highly nonlinear dynamics and long term propagations. Furthermore, valuable additional information about the dynamical system is available from the pattern in which those automatic splits occur. From this pattern it is immediately visible where the system behaves chaotically and where its evolution is smooth. Furthermore, it is possible to deduce the behavior of the system for each region, yielding further insight into the dynamics. In this work, the method is applied to the analysis of an end-of-life disposal trajectory of the INTEGRAL spacecraft.

473-492
Univelt Inc.
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201
Di Lizia, Pierluigi
8a0d7c21-8869-498e-95c8-41a8c8a6dd1a
Armellin, Roberto
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Zazzera, Franco Bernelli
8c213014-c2e4-4a0a-b1f3-a246df0374ad
Makino, Kyoko
273d1542-a2f6-4c1a-b54c-7a5a493151a0
Berz, Martin
f8159a81-aa52-4ba3-8b8f-a672aec96b47
Wittig, Alexander
3a140128-b118-4b8c-9856-a0d4f390b201
Di Lizia, Pierluigi
8a0d7c21-8869-498e-95c8-41a8c8a6dd1a
Armellin, Roberto
61950d5c-3dcf-45f5-b391-7e8c6ffb8e6f
Zazzera, Franco Bernelli
8c213014-c2e4-4a0a-b1f3-a246df0374ad
Makino, Kyoko
273d1542-a2f6-4c1a-b54c-7a5a493151a0
Berz, Martin
f8159a81-aa52-4ba3-8b8f-a672aec96b47

Wittig, Alexander, Di Lizia, Pierluigi, Armellin, Roberto, Zazzera, Franco Bernelli, Makino, Kyoko and Berz, Martin (2015) Long term nonlinear propagation of uncertainties in perturbed geocentric dynamics using automatic domain splitting. In 2nd IAA Conference on Dynamics and Control of Space Systems, 2014. vol. 153, Univelt Inc. pp. 473-492 .

Record type: Conference or Workshop Item (Paper)

Abstract

Current approaches to uncertainty propagation in astrodynamics mainly refer to linearize 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 in highly nonlinear dynamics or long term propagation. We solve this issue by introducing automatic domain splitting. During propagation, the polynomial of the current state is split in two polynomials when its accuracy reaches a given threshold. The resulting polynomials accurately track uncertainties, even in highly nonlinear dynamics and long term propagations. Furthermore, valuable additional information about the dynamical system is available from the pattern in which those automatic splits occur. From this pattern it is immediately visible where the system behaves chaotically and where its evolution is smooth. Furthermore, it is possible to deduce the behavior of the system for each region, yielding further insight into the dynamics. In this work, the method is applied to the analysis of an end-of-life disposal trajectory of the INTEGRAL spacecraft.

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More information

Published date: 2015
Venue - Dates: 2nd International Academy of Astronautics Conference on Dynamics and Control of Space Systems, DyCoSS 2014, Rome, Italy, 2014-03-24 - 2014-03-26

Identifiers

Local EPrints ID: 419783
URI: http://eprints.soton.ac.uk/id/eprint/419783
PURE UUID: 6efb91e0-a700-4838-8c5d-c4418f0824d5
ORCID for Alexander Wittig: ORCID iD orcid.org/0000-0002-4594-0368

Catalogue record

Date deposited: 20 Apr 2018 16:30
Last modified: 20 Jul 2019 00:26

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Contributors

Author: Alexander Wittig ORCID iD
Author: Pierluigi Di Lizia
Author: Franco Bernelli Zazzera
Author: Kyoko Makino
Author: Martin Berz

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