Because of the relatively large set of initial conditions compatible with measured orbit data, great care has to be taken to limit overestimation of the possible range of final coordinates. This is achieved using the approach of Taylor models. Within this framework, it is possible to control the so-called dependency problem as well as the wrapping effect commonly observed in verified integration. This approach yields accuracies that are sufficient to guarantee absence of collisions.
Examples of orbit integrations are given, showing that even relatively large domain boxes can be transported over extended time periods with a relative overestimation in the range of only around 10-5.
M. Berz, K. Makino, J. Hoefkens, Nonlinear Analysis 47 (2001) 179-190
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