On the retrograde motion of a rolling disk

A.V. Borisov^a, b, c, A.A. Kilin^c, Yu.L. Karavaev^c, d
^aMoscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141701, Russian Federation
^bInstitute of Computer Science, ul. Universitetskaya 1, Izhevsk, 426034, Russian Federation
^cUdmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russian Federation
^dIzhevsk State Technical University, Studencheskaya st. 7, Izhevsk, 426069, Russian Federaion

This paper presents theoretical and experimental research explaining the retrograde final-stage rolling of a disk under certain relations between its mass and geometric parameters. Modifying the no-slip model of a rolling disk by including viscous rolling friction provides a qualitative explanation for the disk's retrograde motion. At the same time, the simple experiments described in the paper fully compromise the drag moment as a key reason for the retrograde motion considered, thus disproving some recent hypotheses.

Keywords: retrograde turn, rolling disk, nonholonomic model, rolling friction
PACS: 02.60.Cb, 05.45.−a, 45.40.−f (all)
DOI: 10.3367/UFNe.2017.01.038049
URL: https://ufn.ru/en/articles/2017/9/e/
Web of Science

000417704200005
Scopus

2-s2.0-85020235209
ADS NASA

2017PhyU...60..931B
Citation: Borisov A V, Kilin A A, Karavaev Yu L "On the retrograde motion of a rolling disk" Phys. Usp. 60 931–934 (2017)

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Received: 1st, December 2016, revised: 10th, January 2017, accepted: 17th, January 2017

Оригинал: Борисов А В, Килин А А, Караваев Ю Л «О попятном движении катящегося диска» УФН 187 1003–1006 (2017); DOI: 10.3367/UFNr.2017.01.038049

References (26) ↓ Cited by (20) Similar articles (3)

Jalali M A, Sarebangholi M S, Alam M-R Phys. Rev. E 92 032913 (2015)
Szebehely V Theory Of Orbits, The Restricted Problem Of Three Bbodies (New York: Academic Press, 1967); Per. na russk. yaz., Sebekhei V Teoriya Orbit: Ogranichennaya Zadacha Trekh Tel (M.: Nauka, 1982)
Ruina A "Comments on Euler’s disk and its finite-time singularity by H.K. Moffatt" Unpublished notes (Ithaca, NY: Dept. of Theoretical and Applied Mechanics, Cornell Univ., 2000)
Van den Engh G, Nelson P, Roach J Nature 408 540 (2000)
Petrie D, Hunt J L, Gray C G Am. J. Phys. 70 1025 (2002)
Moffatt H K Nature 404 833 (2000)
Kessler P, O’Reilly O M Regular Chaotic Dynamics 7 49 (2002)
Caps H et al. Phys. Rev. E 69 056610 (2004)
Saje M, Zupan D Multidiscipline Modeling Mater. Struct. 2 49 (2006)
Leine R L Archive Appl. Mech. 79 1063 (2009)
Borisov A V, Mamaev I S, Karavaev Yu L Nonlinear Dynamics 79 2287 (2015)
Ma D, Liu C J. Appl. Mech. 83 061003 (2016)
Borisov A V, Mamaev I S, Kilin A A Regular Chaotic Dynamics 8 201 (2003)
Przybylska M, Rauch-Wojciechowski S Regular Chaotic Dynamics 21 204 (2016)
Srinivasan M, Ruina A Phys. Rev. E 78 066609 (2008)
Or A C SIAM J. Appl. Math. 54 597 (1994)
Cross R Am. J. Phys. 81 280 (2013)
Karavaev Y L, Kilin A A, Borisov A V "The spinning motion of a ring, 2016" https://youtu.be/SEIyoQ0iWdI
Karavaev Y L, Kilin A A, Borisov A V "The spinning motion of a ring after applying adhesive film to it (2016)" https://youtu.be/l9C1KNq3OqU
Karavaev Y L, Kilin A A, Borisov A V "The spinning motion of a ring in a vacuum (2016)" https://youtu.be/VnktVz4H6R0
Karavaev Y L, Kilin A A, Borisov A V "The spinning motion of a ring at atmospheric pressure (2016)" https://youtu.be/s3SiPwxgoIk
Takano H Regular Chaotic Dynamics 19 81 (2014)
Ma D, Liu C, Zhao Z, Zhang H Proc. R. Soc. London A 470 20140191 (2014)
Contensou P Kreiselprobleme Gyrodynamics, Intern. Union Of Theoretical And Applied Mechanics Symp. Celerina, Switzerland, 1962 (Ed. H Ziegler) (Berlin: Springer, 1963) p. 201
Mamaev I S, Ivanova T B Regular Chaotic Dynamics 19 116 (2014)
Ivanova T B, Mamaev I S Prikladnaya Matematika Mekhanika 80 11 (2016); Ivanova T B, Mamaev I S J. Appl. Math. Mech. 80 7 (2016)