Reducing round-off errors in rigid body dynamics

Gilles Vilmart (1, 2)

1 IPSO - Invariant Preserving SOlvers
2 IRMAR - Institut de Recherche Mathématique de Rennes

In several recent publications, numerical integrators based on Jacobi elliptic functions are proposed for solving the equations of motion of the rigid body. Although this approach yields theoretically the exact solution, a standard implementation shows an unexpected linear propagation of round-off errors. We explain how deterministic error contribution can be avoided, so that round-off behaves like a random walk.

Mots clés: Rigid body integrator; Jacobi elliptic functions; Probabilistic error propagation; Long-time integration; Compensated summation; Quaternion; Discrete Moser-Veselov algorithm

Gilles Vilmart. Reducing round-off errors in rigid body dynamics. Journal of Computational Physics, 2008, 227 (15), pp.7083-7088. ⟨10.1016/j.jcp.2008.04.013⟩. ⟨hal-00847927⟩