RSS feeds
РусскийEnglish
Issue 9, 2026
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

2003

 / 

April

←  →

Methodological notes


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.

Fulltext pdf (548 KB)
Fulltext is also available at DOI: 10.1070/PU2003v046n04ABEH001306
PACS: 05.45.−a, 45.10.−b, 45.40.−f (all)
DOI: 10.1070/PU2003v046n04ABEH001306
URL: https://ufn.ru/en/articles/2003/4/c/
000184349400003
Citation: Borisov A V, Mamaev I S "Strange attractors in rattleback dynamics" Phys. Usp. 46 393–403 (2003)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

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 (78) ↓ Similar articles (20)

  1. Bizyaev I A, Berdnikova A S Regul. Chaot. Dyn. 31 (1) 28 (2026)
  2. Collins B W, Hogan S J SIAM J. Appl. Dyn. Syst. 25 (3) 1620 (2026)
  3. Gonchenko S V, Morozov K E Regul. Chaot. Dyn. 31 (1) 53 (2026)
  4. Rai A K, Chandran R R Journal Of Vibration And Control 32 (13-14) 3867 (2026)
  5. Bizyaev I A, Mamaev I S Regul. Chaot. Dyn. 29 (5) 728 (2024)
  6. Kilin A A, Pivovarova E N Regul. Chaot. Dyn. 28 (1) 78 (2023)
  7. Sailer S, Leine R I Proc. R. Soc. A. 479 (2275) (2023)
  8. Takano H Regul. Chaot. Dyn. 28 (2) 227 (2023)
  9. Bizyaev I A, Mamaev I S Regul. Chaot. Dyn. 27 (6) 587 (2022)
  10. Kuleshov A S, Pikunova E N Vestnik St.Petersb. Univ.Math. 55 (2) 203 (2022)
  11. Munitsyna M A Autom Remote Control 83 (3) 325 (2022)
  12. Arioli G, Koch H J Nonlinear Sci 32 (3) (2022)
  13. Sailer S, Leine R I Proc. R. Soc. A. 477 (2256) (2021)
  14. Garc?ea-Agúndez A, Garc?ea-Vallejo D, Freire E Nonlinear Dyn 103 (1) 557 (2021)
  15. Sailer S, Leine R I Nonlinear Dyn 105 (3) 1955 (2021)
  16. Agúndez A G, Garc?ea-Vallejo D, Freire E International Journal Of Mechanical Sciences 198 106392 (2021)
  17. Gonchenko S V Radiophys Quantum El 63 (9-10) 756 (2021)
  18. Sailer S, Eugster S R, Leine R I Regul. Chaot. Dyn. 25 (6) 553 (2020)
  19. Bizyaev I A, Mamaev I S International Journal Of Non-Linear Mechanics 126 103550 (2020)
  20. Gonchenko S V, Gonchenko A S, Kazakov A O Proc. Steklov Inst. Math. 308 (1) 125 (2020)
  21. Gonchenko S V, Gonchenko A S, Kazakov A O ’nру’?ы ’a’?т’?’?’?т’?ch’?с’?’?’?’? ’?’?ст’?тут’? ’?’?’?’?’? ’E. ’B. ’lт’?’?’?’?’?’? 308 135 (2020)
  22. Borisov A V, Mikishanina E A Regul. Chaot. Dyn. 25 (3) 313 (2020)
  23. Kuznetsov S P, Kruglov V P, Borisov A V EPL 132 (2) 20008 (2020)
  24. Mamaev I S, Vetchanin E V 2020 International Conference Nonlinearity, Information and Robotics (NIR), (2020) p. 1
  25. Tudoran Răzvan M, Gîrban Anania Journal Of Mathematical Analysis And Applications 488 (1) 124066 (2020)
  26. Borisov A V, Vetchanin E V, Mamaev I S Russ. J. Math. Phys. 26 (4) 412 (2019)
  27. Gonchenko A S, Gonchenko S V et al Radiophys Quantum El 61 (10) 773 (2019)
  28. Borisov A V, Kilin A A, Mamaev I S American Journal of Physics 87 (11) 935 (2019)
  29. Kruglov V P, Kuznetsov S P Regul. Chaot. Dyn. 24 (6) 725 (2019)
  30. Bizyaev I A, Borisov A V et al Nonlinearity 32 (9) 3209 (2019)
  31. Borisov A V, Kilin A A, Mamaev I S Regul. Chaot. Dyn. 24 (3) 329 (2019)
  32. Liu Ch, Dong L Eur. J. Phys. 40 (3) 035006 (2019)
  33. Awrejcewicz Ja, Kudra G Multibody Syst Dyn 45 (2) 155 (2019)
  34. Gonchenko A S, Samylina E A Radiophys Quantum El 62 (5) 369 (2019)
  35. Bizyaev I A, Borisov A V, Kuznetsov S P Nonlinear Dyn 95 (1) 699 (2019)
  36. Borisov A V, Mamaev I S, Vetchanin E V Regul. Chaot. Dyn. 23 (4) 480 (2018)
  37. Kuznetsov S P Regul. Chaot. Dyn. 23 (2) 178 (2018)
  38. Borisov A V, Kuznetsov S P Regul. Chaot. Dyn. 23 (7-8) 803 (2018)
  39. Bizyaev I A, Borisov A V, Kuznetsov S P EPL 119 (6) 60008 (2017)
  40. Rauch-Wojciechowski S, Przybylska M Regul. Chaot. Dyn. 22 (4) 368 (2017)
  41. Borisov A V, Mamaev I S, Bizyaev I A ’pс’?’?kh’? ’?’?т’?’?’?т’?ch’?с’?’?kh ’?’?у’? 72 (5(437)) 3 (2017)
  42. Kondo Y, Nakanishi H Phys. Rev. E 95 (6) (2017)
  43. Kuznetsov S P EPL 118 (1) 10007 (2017)
  44. Bizyaev I A, Borisov A V, Mamaev I S Regul. Chaot. Dyn. 22 (8) 955 (2017)
  45. Kuznetsov S P, Kruglov V P Proc. Steklov Inst. Math. 297 (1) 208 (2017)
  46. Borisov A V, Kazakov A O, Pivovarova E N Regul. Chaot. Dyn. 21 (7-8) 885 (2016)
  47. Borisov A V, Kazakov A O, Sataev I R Regul. Chaot. Dyn. 21 (7-8) 939 (2016)
  48. Bizyaev I A, Borisov A V, Mamaev I S Regul. Chaot. Dyn. 21 (1) 136 (2016)
  49. Borisov A V, Kuznetsov S P Regul. Chaot. Dyn. 21 (7-8) 792 (2016)
  50. Nanda A, Singla P, Karami M A Journal Of Sound And Vibration 369 195 (2016)
  51. Kozlov V J Dyn Control Syst 22 (4) 713 (2016)
  52. Zhuravlev V F ’pс’?’?kh’? ф’?’?’?ch’?с’?’?kh ’?’?у’? 185 (12) 1337 (2015) [Zhuravlev V F Phys.-Usp. 58 (12) 1218 (2015)]
  53. Karavaev Yu L, Kilin A A Regul. Chaot. Dyn. 20 (2) 134 (2015)
  54. Gonchenko A S, Gonchenko S V Nonlinearity 28 (9) 3403 (2015)
  55. Bizyaev I A, Borisov A V, Kazakov A O Regul. Chaot. Dyn. 20 (5) 605 (2015)
  56. Borisov A V, Karavaev Yu L et al Regul. Chaot. Dyn. 20 (5) 518 (2015)
  57. Kuznetsov S P ’pс’?’?kh’? ф’?’?’?ch’?с’?’?kh ’?’?у’? 185 (12) 1342 (2015) [Kuznetsov S P Phys.-Usp. 58 (12) 1223 (2015)]
  58. Bolsinov A V, Kilin A A, Kazakov A O Journal Of Geometry And Physics 87 61 (2015)
  59. Borisov A V, Mamaev I S Regul. Chaot. Dyn. 20 (5) 553 (2015)
  60. Kozlov V V Regul. Chaot. Dyn. 20 (3) 205 (2015)
  61. Borisov A V, Kazakov A O, Sataev I R Regul. Chaot. Dyn. 19 (6) 718 (2014)
  62. Borisov A V, Kazakov A O, Kuznetsov S P ’pс’?’?kh’? ф’?’?’?ch’?с’?’?kh ’?’?у’? 184 (5) 493 (2014) [Borisov A V, Kazakov A O, Kuznetsov S P Phys.-Usp. 57 (5) 453 (2014)]
  63. Hanias M, Stavrinides S G, Banerjee S The Scientific World Journal 2014 1 (2014)
  64. Gonchenko A, Gonchenko S et al Int. J. Bifurcation Chaos 24 (08) 1440005 (2014)
  65. Riera Ja, Ballester E et al Model. Sci. Educ. Learn. 7 103 (2014)
  66. Isaeva O B, Kuznetsov A S, Kuznetsov S P Phys. Rev. E 87 (4) (2013)
  67. KUDRA G, AWREJCEWICZ JA Int. J. Bifurcation Chaos 21 (10) 2905 (2011)
  68. Borisov A V, Kilin A A, Mamaev I S Regul. Chaot. Dyn. 16 (1-2) 104 (2011)
  69. Ram?erez Rafael, Sadovskaia N Reports On Mathematical Physics 65 (1) 109 (2010)
  70. Dullin H R, Tsygvintsev A V Annales de la Faculté des sciences de Toulouse : Mathématiques 17 (3) 495 (2010)
  71. Chang Ch-M, Ge Zh-M Nonlinear Dyn 60 (4) 551 (2010)
  72. Fernandez O E, Mestdag T, Bloch A M Regul. Chaot. Dyn. 14 (6) 635 (2009)
  73. Borisov A V, Mamaev I S Regul. Chaot. Dyn. 13 (5) 443 (2008)
  74. Krechetnikov R, Marsden J E Rev. Mod. Phys. 79 (2) 519 (2007)
  75. Borisov A V, Kozlov V V, Mamaev I S Regul. Chaot. Dyn. 12 (5) 531 (2007)
  76. Borisov A V, Kilin A A, Mamaev I S Dokl. Phys. 51 (5) 272 (2006)
  77. ’G’?р’?с’?’? ’B ’E, Borisov A V ’? ’?р ’a’?т’?’?. ’?’?’?’?т’?’? 77 (6) 930 (2005)
  78. Borisov A V, Mamaev I S Math Notes 77 (5-6) 855 (2005)
© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions