



@article {grant2012galilean,
	title = {On Galilean connections and the first jet bundle},
	journal = {Central European Journal of Mathematics},
	volume = {10},
	number = {5},
	year = {2012},
	month = {2012/10/01},
	pages = {1889{\textendash}1895},
	publisher = {Springer},
	abstract = {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 {\textemdash} sometimes called KCC-theory. With certain regularity conditions, we show that any such Cartan connection induces {\textquotedblleft}laboratory{\textquotedblright} coordinate systems, and the geodesic equations in this coordinates form a system of second-order ordinary differential equations. We then show the converse {\textemdash} the {\textquotedblleft}fundamental theorem{\textquotedblright} {\textemdash} 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.},
	author = {Grant, James DE and Brad Lackey}
}
