%0 Journal Article %J Central European Journal of Mathematics %D 2012 %T On Galilean connections and the first jet bundle %A Grant, James DE %A Brad Lackey %X We see how the first jet bundle of curves into affine space can be realized as a homogeneous space of the Galilean group. Cartan connections with this model are precisely the geometric structure of second-order ordinary differential equations under time-preserving transformations — sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces “laboratory” coordinate systems, and the geodesic equations in this coordinates form a system of second-order ordinary differential equations. We then show the converse — the “fundamental theorem” — that given such a coordinate system, and a system of second order ordinary differential equations, there exists regular Cartan connections yielding these, and such connections are completely determined by their torsion. %B Central European Journal of Mathematics %I Springer %V 10 %P 1889–1895 %8 2012/10/01 %G eng