The Kapitza pendulum

Rarely does a 'problem' come along that makes you think more than casually about the question of mathematics's reality, and problems in mathematical physics are full of them. I came across one such problem for the first time yesterday, and given its simplicity, thought I should make note of it.

I spotted a paper yesterday with the title 'The Inverted Pendulum as a Classical Analog of the EFT Paradigm'. I've never understood the contents of such papers without assistance from a physicist, but I like to go through them in case a familiar idea or name jumps up that warrants a more thorough follow-up or I do understand something and that helps me understand something else even better.

In this instance, the latter happened, and I discovered the Kapitza pendulum. In 1908, a British mathematician named Andrew Stephenson described the problem but wasn't able to explain it. That happened at the hands of the Russian scientist Pyotr Kapitsa, for whom the pendulum is named, who worked it out in the 1950s.

You are familiar with the conventional pendulum:

Here, the swinging bob is completely stable when it is suspended directly below the pivot, and is unmoving. The Kapitza pendulum is a conventional pendulum whose pivot is rapidly moved up and down. This gives rise to an unusual stable state: when the bob is directly above the pivot! Here's a demonstration: