A simple pendulum is constituted by an inextensible thread to which a mass material point can be hung that can oscillate around a fixed point called a pole. The component of the weight force along the wire counterbalances the tension of the wire itself, while the component of the weight force perpendicular to the wire acts as a return force and produces the oscillatory motion of the pendulum.
The reverse pendulum represents a simple inverted pendulum, rigid, and without a fixed point. The lower part can therefore move to balance the oscillations of the highest part and thus ensure equilibrium; the control problem therefore leads back to wanting to stabilize the position of a rod constrained to a carriage free to move ...
