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 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.