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

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 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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Identifiers

ORCID for Alexander Wittig: orcid.org/0000-0002-4594-0368

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