Propagation of Large Uncertainty Sets in Orbital Dynamics by Automatic Domain Splitting
AbstractCurrent 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
A. Wittig, P. Di Lizia, R. Armellin, K. Makino, F. Bernelli-Zazzera, M. Berz,
Celestial Mechanics and Dynamical Astronomy 122 (2015) 239-261
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