Comparison of splitting algorithms for the rigid body

Abstract: We compare several different second-order splitting algorithms for the asymmetric rigid body, with the aim of determining which one produces the smallest energy error for a given rigid body, namely, for given moments of inertia. The investigation is based on the analysis of the dominant term of the modified Hamiltonian and indicates that different algorithms can produce energy errors which differ by several orders of magnitude. As a byproduct of this analysis we remark that, for the special case of a flat rigid body with moments of inertia proportional to (1, 0.75 0.25), one of the considered algorithms is in fact of order four.