It has long been known that a single pendulum can be maintained stably in
its inverted, or `upside-down' position if its pivot is vibrated up and
down at a suitably high frequency. In 1993 I proved a simple theorem which
shows how the same `trick' can be performed with *any finite number of
linked pendulums, all balanced on top of one another*.

One rather attractive feature of the theorem is that it relates the
stability of the inverted state to just two simple properties of the
*free* oscillations of the system about its *downward-*hanging state.
In this way there is a direct link between the new
theorem and a classical
investigation of multiple pendulums by Daniel Bermoulli, in 1738.

*Proc. Roy. Soc. A Vol 443, pp 239-245, 1993*

(*See also Chapter 12 of *From Calculus to
Chaos, or

radio interview with Thames
Valley FM, 26 Feb 1998)

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