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Strange attractors in rattleback dynamics

 a,  b
a Lomonosov Moscow State University, Vorobevy Gory, Moscow, 119991, Russian Federation
b Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034, Russian Federation

This review is dedicated to the dynamics of the rattleback, a phenomenon with curious physical properties that is studied in nonholonomic mechanics. All known analytical results are collected here, and some results of our numerical simulation are presented. In particular, three-dimensional Poincare maps associated with dynamical systems are systematically investigated for the first time. It is shown that the loss of stability of periodic and quasiperiodic solutions, which gives rise to strange attractors, is typical of the three-dimensional maps related to rattleback dynamics. This explains some newly discovered properties of the rattleback related to the transition from regular to chaotic solutions at certain values of the physical parameters.

Text can be downloaded in Russian. English translation is available on IOP Science.
PACS: 05.45.−a, 45.10.−b, 45.40.−f (all)
DOI: 10.1070/PU2003v046n04ABEH001306
URL: https://ufn.ru/en/articles/2003/4/c/
Citation: Borisov A V, Mamaev I S "Strange attractors in rattleback dynamics" Phys. Usp. 46 393–403 (2003)
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Оригинал: Борисов А В, Мамаев И С «Странные аттракторы в динамике кельтских камней» УФН 173 407–418 (2003); DOI: 10.3367/UFNr.0173.200304d.0407

References (20) Cited by (49) ↓ Similar articles (15)

  1. Bizyaev I A, Borisov A V, Kuznetsov S P Nonlinear Dyn 95 699 (2019)
  2. Liu Ch, Dong L Eur. J. Phys. 40 035006 (2019)
  3. Bizyaev I A, Borisov A V et al Nonlinearity 32 3209 (2019)
  4. Gonchenko A S, Gonchenko S V et al Radiophys Quantum El 61 773 (2019)
  5. Awrejcewicz Ja, Kudra G Multibody Syst Dyn 45 155 (2019)
  6. Borisov A V, Kilin A A, Mamaev I S Regul. Chaot. Dyn. 24 329 (2019)
  7. Kuznetsov S P Regul. Chaot. Dyn. 23 178 (2018)
  8. Borisov A V, Kuznetsov S P Regul. Chaot. Dyn. 23 803 (2018)
  9. Borisov A V, Mamaev I S, Vetchanin E V Regul. Chaot. Dyn. 23 480 (2018)
  10. Borisov A V, Borisov A V i dr Uspekhi Matematicheskikh Nauk 72 3 (2017)
  11. Rauch-Wojciechowski S, Przybylska M Regul. Chaot. Dyn. 22 368 (2017)
  12. Kondo Y, Nakanishi H Phys. Rev. E 95 (6) (2017)
  13. Bizyaev I A, Borisov A V, Mamaev I S Regul. Chaot. Dyn. 22 955 (2017)
  14. Kuznetsov S P EPL 118 10007 (2017)
  15. Kuznetsov S P, Kruglov V P Proc. Steklov Inst. Math. 297 208 (2017)
  16. Bizyaev I A, Borisov A V, Kuznetsov S P EPL 119 60008 (2017)
  17. Kozlov V J Dyn Control Syst 22 713 (2016)
  18. Borisov A V, Kazakov A O, Sataev I R Regul. Chaot. Dyn. 21 939 (2016)
  19. Borisov A V, Kazakov A O, Pivovarova E N Regul. Chaot. Dyn. 21 885 (2016)
  20. Bizyaev I A, Borisov A V, Mamaev I S Regul. Chaot. Dyn. 21 136 (2016)
  21. Borisov A V, Kuznetsov S P Regul. Chaot. Dyn. 21 792 (2016)
  22. Nanda A, Singla P, Karami M A Journal Of Sound And Vibration 369 195 (2016)
  23. Borisov A V, Karavaev Yu L et al Regul. Chaot. Dyn. 20 518 (2015)
  24. Kuznetsov S P Uspekhi Fizicheskikh Nauk 185 1342 (2015) [Kuznetsov S P Phys.-Usp. 58 1223 (2015)]
  25. Bizyaev I A, Borisov A V, Kazakov A O Regul. Chaot. Dyn. 20 605 (2015)
  26. Kozlov V V Regul. Chaot. Dyn. 20 205 (2015)
  27. Karavaev Yu L, Kilin A A Regul. Chaot. Dyn. 20 134 (2015)
  28. Gonchenko A S, Gonchenko S V Nonlinearity 28 3403 (2015)
  29. Borisov A V, Mamaev I S Regul. Chaot. Dyn. 20 553 (2015)
  30. Zhuravlev V F Uspekhi Fizicheskikh Nauk 185 1337 (2015) [Zhuravlev V F Phys.-Usp. 58 1218 (2015)]
  31. Bolsinov A V, Kilin A A, Kazakov A O Journal Of Geometry And Physics 87 61 (2015)
  32. Borisov A V, Kazakov A O, Sataev I R Regul. Chaot. Dyn. 19 718 (2014)
  33. Borisov A V, Kazakov A O, Kuznetsov S P Uspekhi Fizicheskikh Nauk 184 493 (2014) [Borisov A V, Kazakov A O, Kuznetsov S P Phys.-Usp. 57 453 (2014)]
  34. Hanias M, Stavrinides S G, Banerjee S The Scientific World Journal 2014 1 (2014)
  35. Gonchenko A, Gonchenko S et al Int. J. Bifurcation Chaos 24 1440005 (2014)
  36. Riera Ja, Ballester E et al Model. Sci. Educ. Learn. 7 103 (2014)
  37. Isaeva O B, Kuznetsov A S, Kuznetsov S P Phys. Rev. E 87 (4) (2013)
  38. Franti L 11 (2) (2013)
  39. KUDRA GRZEGORZ, AWREJCEWICZ JAN Int. J. Bifurcation Chaos 21 2905 (2011)
  40. Borisov A V, Kilin A A, Mamaev I S Regul. Chaot. Dyn. 16 104 (2011)
  41. Chang Ch-M, Ge Zh-M Nonlinear Dyn 60 551 (2010)
  42. Ramírez R, Sadovskaia N Reports On Mathematical Physics 65 109 (2010)
  43. Fernandez O E, Mestdag T, Bloch A M Regul. Chaot. Dyn. 14 635 (2009)
  44. Borisov A V, Mamaev I S Regul. Chaot. Dyn. 13 443 (2008)
  45. Krechetnikov R, Marsden J E Rev. Mod. Phys. 79 519 (2007)
  46. Borisov A V, Kozlov V V, Mamaev I S Regul. Chaot. Dyn. 12 531 (2007)
  47. Borisov A V, Kilin A A, Mamaev I S Dokl. Phys. 51 272 (2006)
  48. Borisov A V, Borisov A V i dr Matem. Zametki 77 930 (2005)
  49. Borisov A V, Mamaev I S Math Notes 77 855 (2005)

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