Rod in a train: a mechanical problem of H.Whitney, or Much Ado About Nothing

Abstract

In 1941 a mechanical problem about a rod in a moving train (there is a initial position such that rod does not touch the floor while train is moving) was published by R.Courant and H.Robbins in their popular book "What is mathematics?" and attributed to H.Whitney. Many mathematicians, including G.E.Littlewood, A.Broman, T.Poston, I.Stewart, V.Arnold, commented on this problem and its solution based on a continuity argument, and created a lot of confusion. In this paper we follow these developments and discuss at what extent the objections were justified. (In Russian)