  This note investigates the controllability of two unstable second-order
systems that are coupled through a common input. These dynamics occur for
different types of inverted-pendulum systems. Controllability is quantified by
the volume of the state-space that can be reached with unit energy, provided
that the system starts and ends at the origin. It is shown that controllability
is maximized when the ratio between the time constants amounts to the silver
ratio.
