Not quite the Indian Rope trick

Description

The Indian rope trick is stage magic said to have been performed in and around India during the 19th century. The magician would hurl a rope into the air. The rope would stand erect, with no external support. His boy assistant, Jamoora, would climb the rope and then descend. (from Wikipedia)

Now remarkably a single inverted rigid pendulum can be stabilised simply by oscillating the pivot point with a particular frequency and amplitude.

More recently, in 1993 it was shown mathematically that this can be generalised to double, triple etc. pendulums. Indeed in theory any finite number of inverted pendulums can be stabilised. Here is a video showing a triple pendulum:

The case when the number of pendulums goes to infinity (the flexible rope) does not work however, hence one can not quite reproduce the Indian rope trick this way. On the other hand more recent investigations have gone further in this direction.

In this project you will study the mathematics of this remarkable counterintuitive fact. Generalisations could lead towards computer controlled inverted pendulums or more recent work on elastic jointed pendulums. Or indeed one could study other counterintuitive occurences (eg Does a falling slinky spring defy gravity?)

Prerequisites

Mathematical Physics II. Dynamical systems would probably also be useful as a co-requisite.

Resources and references

The following are useful links from which you can find more info: link1, link2, link3
Also the book: From Calculus to Chaos: An introduction to dynamics by David Acheson, Published in August 1997 by Oxford University Press, has a section on this.
The paper investigating N inverted pendulums is here . Some more of the maths behind the falling slinky can be found here here .