Hopping hoop dynamics
In the series about stochastic AUROC, I already stated that the bleeding edge of science is not as distant as one might imagine. Let's again check that a bunch of expressions one can write down without breaking a sweat, can be the subject of a contemporary publication.
The article I used as the title picture for this post was published in the May 2026 issue of the American Journal of Physics 94(5):359–362. DOI:10.1119/5.0291968
Researchgate provides a downloadable pdf. It contains a rigorous analysis of the problem. But let's find some interesting facts here. First of all, the age of this problem is about one century. We can trace it through J.E. Littlewood's book "A mathematician's miscellany". The problem is attributed to H. A. Webb, who lived in 1862–1961. I think we can safely assume that he stated this problem around 1900 and it's like 130 years old.
The next thing which intrigues me, is the following phrase: "Still, these studies have not focused on the ideal, absolutely rigid, massless, and non-slipping hoop originally proposed by Littlewood." I hope that its true. And, if it is, it is wonderful. You always are to check all your assumptions. Like you know that there is a problem, which your professor gives to their students for years. One can assume that this problem and its solution is well-known. Another can run deepresearch and get the result: it is an unpublished result. And make one more publication.
I totally can't get this statement: "We will show that hopping is indeed possible, but if the hoop satisfies the conditions for hopping it will hop at the first instant of release." For me it's totally insane. The reason for the hop is the motion of this hoop and there is no motion at all at the very beginning.
Next time I want to share links on experiments with Littlewood's hopping hoop.