The exact computation of the free rigid body motion and its use in splitting methods

This article investigates the use of the computation of the exact free rigid body motion as a component of splitting methods for rigid bodies subject to external forces. We review various matrix and quaternion representations of the solution of the free rigid body equation which involve Jacobi ellipic functions and elliptic integrals and are amenable to numerical computations. We consider implementations which are exact (i.e., computed to machine precision) and semiexact (i.e., approximated via quadrature formulas). We perform a set of extensive numerical comparisons with state-of-the-art geometrical integrators for rigid bodies, such as the preprocessed discrete Moser-Veselov method. Our numerical simulations indicate that these techniques, combined with splitting methods, can be favorably applied to the numerical integration of torqued rigid bodies.