  In the Randall-Sundrum brane-world scenario and other non-compact
Kaluza-Klein theories, the motion of test particles is higher-dimensional in
nature. In other words, all test particles travel on five-dimensional geodesics
but observers, who are bounded to spacetime, have access only to the 4D part of
the trajectory. Conventionally, the dynamics of test particles as observed in
4D is discussed on the basis of the splitting of the geodesic equation in 5D.
However, this procedure is {\em not} unique and therefore leads to some
problems. The most serious one is the ambiguity in the definition of rest mass
in 4D, which is crucial for the discussion of the dynamics. We propose the
Hamilton-Jacobi formalism, instead of the geodesic one, to study the dynamics
in 4D. On the basis of this formalism we provide an unambiguous expression for
the rest mass and its variation along the motion as observed in 4D. It is
independent of the coordinates and any parameterization used along the motion.
Also, we are able to show a comprehensive picture of the various physical
scenarios allowed in 4D, without having to deal with the subtle details of the
splitting formalism. Moreover we study the extra non-gravitational forces
perceived by an observer in 4D who describes the geodesic motion of a bulk test
particle in 5D. Firstly, we show that the so-called fifth force fails to
account for the variation of rest mass along the particle's worldline.
Secondly, we offer here a new definition that correctly takes into account the
change of mass observed in 4D.
