  This paper presents a counterexample to the conjecture that the semi-explicit
Lie-Newmark algorithm is variational. As a consequence the Lie-Newmark method
is not well-suited for long-time simulation of rigid body-type mechanical
systems. The counterexample consists of a single rigid body in a static
potential field, and can serve as a test of the variational nature of other
rigid-body integrators.

Numerical Analysis