A Kapitza's pendulum shows that it is possible to stabilize an inverted pendulum by making its base oscillate vertically. This action seems to introduce an inertial effect which will produce an attractor about the upright vertical position. This work shows that the upright posture of the trunk achieved while walking can be explained using a combination of a vertical oscillation and an angular stiffness regulation at the pelvis. This is shown with an estimated oscillation and stiffness obtained from video recordings of an unimpaired and a Parkinsoninan gaits. By simulating the dynamic model of the pendulum for a range of parameters, a series of stability conditions are found. They show that the introduction of the vertical oscillation results in a fast stabilization of the trunk and point to control strategies which rely on the system's dynamics.