A numerical test of long-time stability for rigid body integrators

In the context of Hamiltonian ODEs, a necessary condition for an integrator to be symplectic or conjugate-symplectic is that it nearly preserves the exact Hamiltonian. This paper introduces a numerical test of this necessity for rigid body methods. It turns out that several rigid body integrators proposed in literature fail this test. Hence, these integrators should be used with caution for long-time simulation