This work investigates the passivity-based control of a class of underactuated mechanical systems for which the momenta are not measurable. To this end, a port-Hamiltonian formulation and a passivity-based control approach are employed. The main contribution is a new dynamic extension of the interconnection-and-damping assignment passivity-based control that only depends on the generalized position. Numerical simulations on an Acrobot system demonstrate that the proposed approach allows stabilizing the prescribed equilibrium by relying only on position feedback.