We extend the method of controlled Lagrangians (CL) to include potential sh
aping, which achieves complete state-space asymptotic stabilization of mech
anical systems. The CL method deals with mechanical systems with symmetry a
nd provides symmetry-preserving kinetic shaping and feedback-controlled dis
sipation for state-space stabilization in all but the symmetry variables. P
otential shaping complements the kinetic shaping by breaking symmetry and s
tabilizing the remaining state variables. The approach also extends the met
hod of controlled Lagrangians to include a class of mechanical systems with
out symmetry such as the inverted pendulum on a cart that travels along an
incline.