Tales from the ArXiv: Centenary of Emmy Noether's Invariante Variationsprobleme

This article commemorates the centenary of Emmy Noether's article Invariante Variationsprobleme.

Title: On the Wonderfulness of Noether's Theorems, 100 Years Later, and Routh Reduction

Author: Raphaël Leone

Abstract: This paper is written in honour of the centenary of Emmy Amalie Noether's famous article entitled Invariante Variationsprobleme. It firstly aims to give an exposition of what we believe to be the most significant and elegant issues regarding her theorems, through the lens of classical mechanics. Despite the limitation to this field, we try to illustrate the key ideas of her work in a rather complete and pedagogical manner which, we hope, presents some original aspects. The notion of symmetry coming naturally with the idea of simplification, the last part is devoted to the interplay between Noether point symmetries and the reduction procedure introduced by Edward John Routh in 1877.

Harmonographs

A harmonograph is a drawing device that is constructed of coupled pendula. Here are some instructions for how to make one based on triple pendula. Oxford's Museum of the History of Science apparently houses this one, although it wasn't there the last time I visited. I also remember seeing something along these lines (or maybe it is even an example of one?) at KITP.

And, of course, this automatically makes me think of the Spirograph drawing set that I had as a kid.

(Tip of the cap to the National Museum of Mathematics.)

One of My Contributions to Physics

The quote "Cycles. Is there anything they can’t do?" certainly sounds like something that I would say or write sarcastically, though I no longer remember when I said (or wrote) this. Anyway, you can find it at the top of Chapter 13 of Chaos: Classical and Quantum.

Classical Versus Quantum

Again using Google's new tool, one can see transitions between ordinary English usage and jargon.