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A new concept of stability in orbit propagation, useful for quantifying numerical errors

A new concept of stability in orbit propagation, useful for quantifying numerical errors
A new concept of stability in orbit propagation, useful for quantifying numerical errors

We present the concept of topological stability in the numerical propagation of orbits, and show how it results in a useful new method for measuring the global numerical error of an orbit propagation. The concept applies to any problem in orbital dynamics. Moreover, it can be extended to any three-dimensional system of differential equations of second order. In order to assess the topological stability of a given integration a special metric is introduced, which can be used to estimate the numerical errors robustly. The method is particularly well suited for dealing with strongly perturbed and chaotic systems. The construction is based on the constraint imposed by the Hopf map that supports the Kustaanheimo-Stiefel transformation. Generic concepts of stability are translated to KS space.

1329-1348
Univelt Inc.
Roa, Javier
d00b2b50-8415-4dc0-b1b9-ee980458e35d
Urrutxua, Hodei
ec73b9d7-654f-4db7-9ff3-68ad05543cfe
Peláez, Jesús
4d93acac-5ae9-4a59-8550-bcfbb392af3f
Roa, Javier
d00b2b50-8415-4dc0-b1b9-ee980458e35d
Urrutxua, Hodei
ec73b9d7-654f-4db7-9ff3-68ad05543cfe
Peláez, Jesús
4d93acac-5ae9-4a59-8550-bcfbb392af3f

Roa, Javier, Urrutxua, Hodei and Peláez, Jesús (2018) A new concept of stability in orbit propagation, useful for quantifying numerical errors. In ASTRODYNAMICS 2017. vol. 162, Univelt Inc. pp. 1329-1348 .

Record type: Conference or Workshop Item (Paper)

Abstract

We present the concept of topological stability in the numerical propagation of orbits, and show how it results in a useful new method for measuring the global numerical error of an orbit propagation. The concept applies to any problem in orbital dynamics. Moreover, it can be extended to any three-dimensional system of differential equations of second order. In order to assess the topological stability of a given integration a special metric is introduced, which can be used to estimate the numerical errors robustly. The method is particularly well suited for dealing with strongly perturbed and chaotic systems. The construction is based on the constraint imposed by the Hopf map that supports the Kustaanheimo-Stiefel transformation. Generic concepts of stability are translated to KS space.

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AAS-17-613 (Preprint) - Author's Original
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Published date: 2018
Venue - Dates: AAS/AIAA Astrodynamics Specialist Conference, 2017, ,, United States, 2017-08-19 - 2017-08-23

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Local EPrints ID: 422218
URI: http://eprints.soton.ac.uk/id/eprint/422218
PURE UUID: 5af2a2e3-0fac-4691-9aa8-caf565125a54

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Date deposited: 19 Jul 2018 16:30
Last modified: 09 Oct 2020 16:36

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