Letters to the editors

On the validity of nonholonomic model of the rattleback

Kotel'nikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences, Saratov Branch, ul. Zelenaya 38, Saratov, 410019, Russian Federation

In connection with the problem of a convex-shaped solid body on a rough horizontal plane (the rattleback or Celtic stone), the paper discusses the validity of the nonholonomic model, which postulates that the contact point has a zero velocity and hence friction performs no mechanical work. While abstract, this model is undoubtedly constructive, similar to many idealizations commonly used in science. Despite its energy-conserving nature, the model does not obey Liouville's theorem on phase volume conservation, thus allowing the occurrence in the phase space of objects characteristic for dissipative dynamics (attractors) and thereby leading to phenomena like the spontaneous reversal of rotations. Nonholonomic models, intermediate between conservative and dissipative systems, should take their deserved place in the general picture of the modern theory of dynamical systems.

Fulltext is available at IOP
Keywords: rattleback, solid body, nonholonomic model, attractor
PACS: 05.45.−a, 45.40.−f (all)
DOI: 10.3367/UFNe.0185.201512h.1342
Citation: Kuznetsov S P "On the validity of nonholonomic model of the rattleback" Phys. Usp. 58 1223–1224 (2015)
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Received: 8th, October 2015, 8th, October 2015

Оригинал: Кузнецов С П «К вопросу о правомерности неголономной модели динамики кельтского камня» УФН 185 1342–1344 (2015); DOI: 10.3367/UFNr.0185.201512h.1342

References (21) ↓ Cited by (4) Similar articles (7)

  1. Zhuravlev V F Usp. Fiz. Nauk 185 1337 (2015); Zhuravlev V F Phys. Usp. 58 (12) (2015)
  2. Borisov A V, Mamaev I S Usp. Fiz. Nauk 173 407 (2003); Borisov A V, Mamaev I S Phys. Usp. 46 393 (2003)
  3. Borisov A V, Kazakov A O, Kuznetsov S P Usp. Fiz. Nauk 184 493 (2014); Borisov A V, Kazakov A O, Kuznetsov S P Phys. Usp. 57 453 (2014)
  4. Loskutov A Yu Usp. Fiz. Nauk 180 1305 (2010); Loskutov A Phys. Usp. 53 1257 (2010)
  5. Afraimovich V S et al. Regul. Chaotic Dyn. 19 (4) 435 (2014)
  6. Kuznetsov S P Dinamicheskii Khaos (M.: Fizmatlit, 2006)
  7. Zhuravlev V F, Klimov D M Izv. RAN. Mekhanika Tverdogo Tela (3) 8 (2008); Zhuravlev V Ph, Klimov D M Mech. Solids 43 320 (2008)
  8. Feynman R P, Leighton R B, Sands M The Feynman Lectures On Physics (Reading, Mass.: Addison-Wesley Publ. Co., 1963); Per. na russk. yaz., Feinman R, Leiton R, Sends M Feinmanovskie Lektsii Po Fizike (M.: Mir, 1967)
  9. Lamb H Hydrodynamics (Cambridge: The Univ. Press, 1930); Per. na russk. yaz., Lamb G Gidrodinamika (M. - L.: OGIZ, 1947)
  10. Sokolovskii Yu I Teoriya Otnositel’nosti v Elementarnom Izlozhenii (M.: Nauka, 1964); Per. 1-go russk. izd., Sokolovskii Iu I The Special Theory Of Relativity (Delhi: Hindustan Publ. Corp., 1962)
  11. Hertz H Prinzipien Der Mechanik In Neuem Zusammenhange Dargestellt (Leipzig: Johann Ambrosius Barth, 1894); Per. na angl. yaz., Hertz H The Principles Of Mechanics Presented In A New Form (Mineola, N.Y.: Dover Publ., 2003); Per. na russk. yaz., Gerts G Printsipy Mekhaniki, Izlozhennye v Novoi Svyazi (Pod obshch. red. I I Artobolevskogo) (M.: Izd-vo AN SSSR, 1959)
  12. Neimark Yu I, Fufaev N A Dinamika Negolonomnykh Sistem (M.: Nauka, 1967); Per. na angl. yaz., Neimark Ju I, Fufaev N A Dynamics Of Nonholonomic Systems (Providence, R.I.: American Mathematical Society, 1972)
  13. Mei F Appl. Mech. Rev. 53 (11) 283 (2000)
  14. Borisov A V, Mamaev I S, Bizyaev I A Regul. Chaotic Dyn. 18 (3) 277 (2013)
  15. Borisov A V, Kazakov A O, Sataev I R Regul. Chaotic Dyn. 19 (6) 718 (2014)
  16. Lorenz E N J. Atmos. Sci. 20 (2) 130 (1963)
  17. Gonchenko A S, Gonchenko S V, Kazakov A O Regul. Chaotic Dyn. 18 (5) 521 (2013)
  18. Feigenbaum M J J. Stat. Phys. 19 (1) 25 (1978)
  19. Baillieul J, Sastry S S, Sussmann H J (Eds) Essays On Mathematical Robotics (The IMA Volumes in Mathematics and its Applications) Vol. 104 (New York: Springer-Verlag, 2012)
  20. Becker F et al. Regul. Chaotic Dyn. 18 (1 - 2) 63 (2013)
  21. Svinin M, Morinaga A, Yamamoto M Regul. Chaotic Dyn. 18 (1 - 2) 126 (2013)

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