  We prove that for every polynomial ODE there exists a Carnot group where the
trajectories of the ODE lift to abnormal curves. The proof defines an explicit
construction to determine a covector for the resulting abnormal curves. Using
this method we give new examples of abnormal curves in Carnot groups of high
step. As a byproduct of the argument, we also prove that concatenations of
abnormal curves have abnormal lifts.
