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

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 di erential 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.