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This paper presents a counterexample to the conjecture that the semi-explicitLie-Newmark algorithm is variational. As a consequence the Lie-Newmark methodis not well-suited for long-time simulation of rigid body-type mechanicalsystems. The counterexample consists of a single rigid body in a staticpotential field, and can serve as a test of the variational nature of otherrigid-body integrators.

A counterexample showing the semi-explicit Lie-Newmark algorithm is not variational