  Recently, Morrison and Updike showed that many dissipative systems are
naturally described as possessing a Riemann curvature-like bracket, which
similar to the Poisson bracket, generates the dissipative equations of motion
once suitable generators are chosen. In this paper, we use geometry to
construct and explore the dynamics of these new brackets. Specifically, we
consider the dynamics of a heavy top with dissipation imposed by a Euclidian
contravariant curvature. We find that the equations of motion, despite their
rather formal motivation, naturally generalize the energy-conserving
dissipation considered by Matterasi and Morrison. In particular, with suitable
initial conditions, we find that the geometrically motivated equations of
motion cause the top to relax to rotation about a principal axis.
