  In this paper we propose a new approach to matter dynamics in compactified
Kaluza-Klein theories. We discard the idea that the motion is geodesic and
perform a simultaneous reduction of matter geometry defining the test particle
via a multipole approach. In the resulting dynamics the tower of huge massive
modes is removed, without giving up the compactification scenario. Such an
approach yields a consistent modified gravity theory with source. Some
scenarios and applications to dark energy problem are sketched.
