  We construct a generalized dynamics for particles moving in a symmetric
space-time, i.e. a space-time admitting one or more Killing vectors. The
generalization implies that the effective mass of particles becomes dynamical.
We apply this generalized dynamics to the motion of test particles in a static,
spherically symmetric metric. A significant consequence of the new framework is
to generate an effective negative pressure on a cosmological surface whose
expansion is manifest by the particle trajectory via embedding geometry
\cite{bwg,embed2,embed,pal}. This formalism thus may give rise to a source for
dark energy in modeling the late accelerating universe.
