  A control system $\dot{q} = f(q,u)$ is said to be trivializable if there
exists local coordinates in which the system is feedback equivalent to a
control system of the form $\dot{q} = f(u)$. In this paper we characterize
trivializable control systems and control systems for which, up to a feedback
transformation, $f$ and $\partial f/\partial u$ commute. Characterizations are
given in terms of feedback invariants of the system (its control curvature and
its centro-affine curvature) and thus are completely intrinsic. To conclude we
apply the obtained results to Zermelo-like problems on Riemannian manifolds.
