• shareshare
  • link
  • cite
  • add
auto_awesome_motion View all 4 versions
Publication . Preprint . Article . 2019

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

Shen, Alexander;
Open Access
Published: 29 Oct 2019
Publisher: HAL CCSD
Country: France

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)

(In Russian) version 2: some typos corrected


[INFO.INFO-IT]Computer Science [cs]/Information Theory [cs.IT], [MATH.MATH-LO]Mathematics [math]/Logic [math.LO], [MATH.MATH-HO]Mathematics [math]/History and Overview [math.HO], [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - History and Overview, Mathematics - Dynamical Systems, 34A26, 37N05, History and Overview (math.HO), Dynamical Systems (math.DS), FOS: Mathematics

Related Organizations
16 references, page 1 of 2

[3] С. В. Болотин, В. В. Козлов, Вариационное исчисление в целом, существование траекторий в области с границей и задача Уитни о перевернутом маятнике, Известия РАН, Сер. матем., 2015, том 79, выпуск 5, 39-46, http://www.mathnet. ru/links/517f47a75c35b951a03b01b699d9abef/im8413.pdf

[4] What Is Mathematics? An Elementary Approach to Ideas and Methods. Reviewed by Brian E. Blank, Notices of the AMS, December 2001, 1325-1329, https://www.ams. org/notices/200111/rev-blank.pdf

[5] Arne Broman, A mechanical problem by H. Whitney, Nordisk Matematisk Tidskrift, 6(2) p. 78-82 (1958). Published by: Mathematica Scandinavica, https://www.jstor. org/stable/24524634

[6] Reviewed Work: What Is Mathematics? by Richard Courant, Herbert Robbins, Ian Stewart. Review by: Leonard Gillman. The American Mathematical Monthly, 105(5), 485-488 (May 1998),

[7] Oleg Zubelevich, Bounded Solutions to the System of 2-nd Order ODE and the Whitney pendulum, См. также журнальный вариант: Applicationes Mathematicae, 42, 159-165 (2015), DOI: 10.4064/am42-2-3. [OpenAIRE]

[8] Richard Courant, Herbert Robbins, What is Mathematics? An elementary approach to ideas and methods. London, New York, Toronto: Oxford University press. 1941. Fourth printing: 1948. Ninth printing: 1958. Tenth printing: 1960. Eleventh printing: 1961.

[9] The Lever of Mahomet, by Richard Courant and Herbert Robbins, p. 2412 of the antology The World of Mathematics, A small library of the literature of mathematics from A'h-mos´e the Scribe to Albert Einstein, presented with commentaries and notes by James R. Newman, London, George Allen and Unwin, Ltd, 1960.

[10] Richard Courant and Herbert Robbins, revised by Ian Stewart, What is mathematics? An elementary approach to ideas and methods, 2nd edition, 1996, Oxford University Press. (В книге указано: First published in 1941 by Oxford University Press. First issued as Oxford University Press paperback, 1978. First published as a second edition, 1996.)

[11] J. E. Littlewood, A Mathematician's Miscellany. London: Methuen & Co., Ltd., 1953. Русский перевод: Дж. Литлвуд, Математическая смесь, перевод В. И. Левина, М.: Физматгиз,1962. Переиздания: 2-е, стереотипное, 1965, 3-е, 1973, 4-е, стерео- типное, 1978, 5-е, исправленное, 1990.

[12] И. Ю. Полехин, Примеры использования топологических методов в задаче о пе- ревернутом маятнике на подвижном основании, Нелинейная динамика, 10(4), 465- 472 (2014), paperid=457