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Reducing round-off errors in rigid body dynamics

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G. Vilmart

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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.

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Key Words. rigid body integrator, Jacobi elliptic functions, probabilistic error propagation, long-time integration, compensated summation, quaternion, Discrete Moser–Veselov algorithm.

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