  The motion of a dynamical system on an $n$-dimensional configuration space
may be regarded as the lightlike shadow of null geodsics moving in an $(n+2)$
dimensional spacetime known as its Einsenhart-Duval lift. In this paper it is
shown that if the configuration space is $n$-dimensional Euclidean space, and
in the absence of magnetic type forces, the Eisenhart-Duval lift may be
regarded as an $(n+1)$-brane moving in a flat $(n+4)$ -dimensional space with
two times. If the Eisenhart-Duval lift is Ricci flat, then the $(n+1)$-brane
moves in such a way as to extremise its spacetime volume. A striking example is
provided by the motion of $N$ point particles moving in three-dimensional
Euclidean space under the influence of their mutual gravitational attraction.
Embeddings with curved configuration space metrics and velocity dependent
forces are also be constructed. Some of the issues arising from the two times
are addressed.
