... DRAFT30CHAPTER 3. THE INVERTED PENDULUM 3.2.3 The Simple Inverted Pendulum Our model for the inverted pendulum is shown in Figure 3.1. Assumingfor the moment that the pendulum leg has zero mass, then gravity ... case is the ratio of the motion of the pendulum bob to the motion of the top support. Since H is complex, it gives the ratio of the amplitudes of the motions and their relative phase.For the simple ... Mgθwhere Fperpis the component of the gravitational force perpendicular to the leg, and M is the mass at the end of the leg. The force is positive,so gravity tends to make the inverted pendulum tip...