  A class of generalized Taub-NUT gravitational instantons is reported in five
- dimensional Einstein gravity coupled to a non-linear sigma model. The
geodesic dynamics of a spinless particle of unit mass on these static
gravitational instantons is studied. This is accomplished by finding a
generalized Runge-Lenz vector. Unlike the Kepler problem, or, the dynamics of a
spinless particle on the familiar Taub-NUT gravitational instantons, the orbits
are not conic sections.
