Abstract
The problem of nonlinear uncertainty propagation represents a crucial issue in celestial mechanics. In this paper a method for nonlinear propagation of uncertainties based on differential algebra is presented. Working in the differential algebra framework enables a general approach to nonlinear uncertainty propagation that can provide high estimate accuracy with low computational burden. The nonlinear mapping of the statistics is here shown adopting the two-body problem as working framework, including coordinate system transformations. The general feature of the proposed method is also demonstrated by presenting long-term integrations in a complex dynamical framework, such as the n-body problem or the HANDE model.