Feedback linearization is a technique that globally transforms a nonlinear system into a linear one. A feedback control law is then applied to the transformed system so as to achieve global asymptotical stable closed-loop dynamics. The construction of the required elements can be simplified if suitable equivalence classes of vectorfields and associated submanifolds are properly chosen. This leads to quotient vector bundles, and quotient submanifolds that foliates the original manifold into a nested sequence of foliations. The construction is performed both analytically and numerically. The interesting aspect of the construction is that it can be applied to systems that are not feedback linearizable. It also helps circumventing singularities in a variety of applications, especially in the case of the field controlled DC motor.