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We derive the path integral action for a particle moving in three dimensionalfuzzy space. From this we extract the classical equations of motion. Theseequations have rather surprising and unconventional features: They predict acut-off in energy, a generally spatial dependent limiting speed, orbitalprecession remarkably similar to the general relativistic result, flat velocitycurves below a length scale determined by the limiting velocity and includedmass, displaced planar motion and the existence of two dynamical branches ofwhich only one reduces to Newtonian dynamics in the commutative limit. Thesefeatures place strong constraints on the non-commutative parameter andcoordinate algebra to avoid conflict with observation and may provide astringent observational test for this scenario of non-commutativity.

Classical dynamics on three dimensional fuzzy space: Connecting the short and long length scales