  For geodesic motion of a particle in a stationary spacetime the $U_0$
component of particle 4-velocity is constant and is considered to be a
conserved mechanical energy. We show that this concept of a conserved
mechanical energy can be extended to particles that move under the influence of
a ``normal force,'' a force that, in the stationary frame, is orthogonal to the
motion of the particle. We illustrate the potential usefulness of the concept
with a simple example.
