From the current literature

On the retrograde motion of a rolling disk

 a, b, c,  c,  c, d
a Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141701, Russian Federation
b Institute of Computer Science, ul. Universitetskaya1, Izhevsk, 426034, Russian Federation
c Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russian Federation
d Izhevsk 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.

Fulltext is available at IOP
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
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, 17th, January 2017

:   ,   ,    « » 187 1003–1006 (2017); DOI: 10.3367/UFNr.2017.01.038049

References (26) ↓ Cited by (15) Similar articles (2)

  1. Jalali M A, Sarebangholi M S, Alam M-R Phys. Rev. E 92 032913 (2015)
  2. 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)
  3. Ruina A "Comments on Euler’s disk and its finite-time singularity by H.K. Moffatt" Unpublished notes (Ithaca, NY: Dept.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)
  4. Van den Engh G, Nelson P, Roach J Nature 408 540 (2000)
  5. Petrie D, Hunt J L, Gray C G Am. J. Phys. 70 1025 (2002)
  6. Moffatt H K Nature 404 833 (2000)
  7. Kessler P, O’Reilly O M Regular Chaotic Dynamics 7 49 (2002)
  8. Caps H et al. Phys. Rev. E 69 056610 (2004)
  9. Saje M, Zupan D Multidiscipline Modeling Mater. Struct. 2 49 (2006)
  10. Leine R L Archive Appl. Mech. 79 1063 (2009)
  11. Borisov A V, Mamaev I S, Karavaev Yu L Nonlinear Dynamics 79 2287 (2015)
  12. Ma D, Liu C J. Appl. Mech. 83 061003 (2016)
  13. Borisov A V, Mamaev I S, Kilin A A Regular Chaotic Dynamics 8 201 (2003)
  14. Przybylska M, Rauch-Wojciechowski S Regular Chaotic Dynamics 21 204 (2016)
  15. Srinivasan M, Ruina A Phys. Rev. E 78 066609 (2008)
  16. Or A C SIAM J. Appl. Math. 54 597 (1994)
  17. Cross R Am. J. Phys. 81 280 (2013)
  18. Karavaev Y L, Kilin A A, Borisov A V "The spinning motion of a ring, 2016"
  19. Karavaev Y L, Kilin A A, Borisov A V "The spinning motion of a ring after applying adhesive film to it (2016)"
  20. Karavaev Y L, Kilin A A, Borisov A V "The spinning motion of a ring in a vacuum (2016)"
  21. Karavaev Y L, Kilin A A, Borisov A V "The spinning motion of a ring at atmospheric pressure (2016)"
  22. Takano H Regular Chaotic Dynamics 19 81 (2014)
  23. Ma D, Liu C, Zhao Z, Zhang H Proc. R. Soc. London A 470 20140191 (2014)
  24. Contensou P Kreiselprobleme Gyrodynamics, Intern. Union Of Theoretical And Applied Mechanics Symp. Celerina, Switzerland, 1962 (Ed. H Ziegler) (Berlin: Springer, 1963) p. 201
  25. Mamaev I S, Ivanova T B Regular Chaotic Dynamics 19 116 (2014)
  26. 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)

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