Reducing round-off errors in rigid body dynamics
G. Vilmart
Abstract. 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.
Key Words. rigid body integrator, Jacobi elliptic functions, probabilistic
error propagation, long-time integration, compensated summation, quaternion, Discrete
MoserVeselov algorithm.