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Generalized particle dynamics: modifying the motion of particles and branes

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.