on Q → → R is defined as a holonomic connection ξ ξ on a jet bundle J 1 Q → → R . This equation also is represented by a connection on an affine jet bundle J 1 Q → → Q . Due to the canonical embedding J 1 Q → → T Q , it is equivalent to a geodesic equation on the tangent bundle T Q of Q . A free motion equation in non-autonomous mechanics exemplifies a second-order non-autonomous dynamic equation.