The Discrete Moser--Veselov algorithm for the free Rigid Body, revisited

In this paper we revisit the Moser–Veselov description for the free Rigid Body, which, in the 3×3 case, can be implemented as an explicit, second order, integrable approximation of the continuous solution. By backward error analysis, we study the modified vector field which is integrated exactly by the discrete algorithm. We deduce that the discrete Moser–Veselov (DMV) is well approximated to higher order by time-reparametrizations of the continuous equations (modified vector field). We use the modified vector field to preprocess the initial data to the DMV and show the equivalence of the DMV algorithm and the RATTLE algorithm. Numerical integration with these preprocessed initial data is several order of magnitude more accurate of the original DMV and RATTLE approach.