RSS feeds
РусскийEnglish
Issue 4, 2024
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 (74) ↓ Similar articles (16)

  1. Kilin A A, Pivovarova E N Regul. Chaot. Dyn. 28 78 (2023)
  2. Takano H Regul. Chaot. Dyn. 28 227 (2023)
  3. Sailer S, Leine R I Proc. R. Soc. A. 479 (2275) (2023)
  4. Kuleshov A S, Pikunova E N Vestnik St.Petersb. Univ.Math. 55 203 (2022)
  5. Arioli G, Koch H J Nonlinear Sci 32 (3) (2022)
  6. Munitsyna M A Autom Remote Control 83 325 (2022)
  7. Bizyaev I A, Mamaev I S Regul. Chaot. Dyn. 27 587 (2022)
  8. Sailer S, Leine R I Proc. R. Soc. A. 477 (2256) (2021)
  9. Gonchenko S V Radiophys Quantum El 63 756 (2021)
  10. García-Agúndez A, García-Vallejo D, Freire E Nonlinear Dyn 103 557 (2021)
  11. Sailer S, Leine R I Nonlinear Dyn 105 1955 (2021)
  12. Agúndez A G, García-Vallejo D, Freire E International Journal Of Mechanical Sciences 198 106392 (2021)
  13. Mamaev I S, Vetchanin E V 2020 International Conference Nonlinearity, Information and Robotics (NIR), (2020) p. 1
  14. Kuznetsov S P, Kruglov V P, Borisov A V EPL 132 20008 (2020)
  15. Sailer S, Eugster S R, Leine R I Regul. Chaot. Dyn. 25 553 (2020)
  16. Tudoran R M, Gîrban A Journal Of Mathematical Analysis And Applications 488 124066 (2020)
  17. Gonchenko S V, Gonchenko A S, Kazakov A O Trudy Matematicheskogo Instituta Imeni V. A. Steklova 308 135 (2020)
  18. Gonchenko S V, Gonchenko A S, Kazakov A O Proc. Steklov Inst. Math. 308 125 (2020)
  19. Borisov A V, Mikishanina E A Regul. Chaot. Dyn. 25 313 (2020)
  20. Bizyaev I A, Mamaev I S International Journal Of Non-Linear Mechanics 126 103550 (2020)
  21. Bizyaev I A, Borisov A V, Kuznetsov S P Nonlinear Dyn 95 699 (2019)
  22. Gonchenko A S, Gonchenko S V et al Radiophys Quantum El 61 773 (2019)
  23. Gonchenko A S, Samylina E A Radiophys Quantum El 62 369 (2019)
  24. Liu Ch, Dong L Eur. J. Phys. 40 035006 (2019)
  25. Borisov A V, Kilin A A, Mamaev I S 87 935 (2019)
  26. Kruglov V P, Kuznetsov S P Regul. Chaot. Dyn. 24 725 (2019)
  27. Bizyaev I A, Borisov A V et al Nonlinearity 32 3209 (2019)
  28. Borisov A V, Kilin A A, Mamaev I S Regul. Chaot. Dyn. 24 329 (2019)
  29. Borisov A V, Vetchanin E V, Mamaev I S Russ. J. Math. Phys. 26 412 (2019)
  30. Awrejcewicz Ja, Kudra G Multibody Syst Dyn 45 155 (2019)
  31. Borisov A V, Kuznetsov S P Regul. Chaot. Dyn. 23 803 (2018)
  32. Kuznetsov S P Regul. Chaot. Dyn. 23 178 (2018)
  33. Borisov A V, Mamaev I S, Vetchanin E V Regul. Chaot. Dyn. 23 480 (2018)
  34. Kuznetsov S P, Kruglov V P Proc. Steklov Inst. Math. 297 208 (2017)
  35. Borisov A V, Mamaev I S, Bizyaev I A Uspekhi Matematicheskikh Nauk 72 3 (2017)
  36. Bizyaev I A, Borisov A V, Kuznetsov S P EPL 119 60008 (2017)
  37. Rauch-Wojciechowski S, Przybylska M Regul. Chaot. Dyn. 22 368 (2017)
  38. Kuznetsov S P EPL 118 10007 (2017)
  39. Kondo Y, Nakanishi H Phys. Rev. E 95 (6) (2017)
  40. Bizyaev I A, Borisov A V, Mamaev I S Regul. Chaot. Dyn. 22 955 (2017)
  41. Borisov A V, Kazakov A O, Pivovarova E N Regul. Chaot. Dyn. 21 885 (2016)
  42. Kozlov V J Dyn Control Syst 22 713 (2016)
  43. Borisov A V, Kuznetsov S P Regul. Chaot. Dyn. 21 792 (2016)
  44. Nanda A, Singla P, Karami M A Journal Of Sound And Vibration 369 195 (2016)
  45. Bizyaev I A, Borisov A V, Mamaev I S Regul. Chaot. Dyn. 21 136 (2016)
  46. Borisov A V, Kazakov A O, Sataev I R Regul. Chaot. Dyn. 21 939 (2016)
  47. Zhuravlev V F Uspekhi Fizicheskikh Nauk 185 1337 (2015) [Zhuravlev V F Phys.-Usp. 58 1218 (2015)]
  48. Bolsinov A V, Kilin A A, Kazakov A O Journal Of Geometry And Physics 87 61 (2015)
  49. Kuznetsov S P Uspekhi Fizicheskikh Nauk 185 1342 (2015) [Kuznetsov S P Phys.-Usp. 58 1223 (2015)]
  50. Borisov A V, Mamaev I S Regul. Chaot. Dyn. 20 553 (2015)
  51. Karavaev Yu L, Kilin A A Regul. Chaot. Dyn. 20 134 (2015)
  52. Borisov A V, Karavaev Yu L et al Regul. Chaot. Dyn. 20 518 (2015)
  53. Bizyaev I A, Borisov A V, Kazakov A O Regul. Chaot. Dyn. 20 605 (2015)
  54. Kozlov V V Regul. Chaot. Dyn. 20 205 (2015)
  55. Gonchenko A S, Gonchenko S V Nonlinearity 28 3403 (2015)
  56. Gonchenko A, Gonchenko S et al Int. J. Bifurcation Chaos 24 1440005 (2014)
  57. Riera Ja, Ballester E et al Model. Sci. Educ. Learn. 7 103 (2014)
  58. 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)]
  59. Hanias M, Stavrinides S G, Banerjee S The Scientific World Journal 2014 1 (2014)
  60. Borisov A V, Kazakov A O, Sataev I R Regul. Chaot. Dyn. 19 718 (2014)
  61. Isaeva O B, Kuznetsov A S, Kuznetsov S P Phys. Rev. E 87 (4) (2013)
  62. Franti L 11 (2) (2013)
  63. Borisov A V, Kilin A A, Mamaev I S Regul. Chaot. Dyn. 16 104 (2011)
  64. KUDRA GRZEGORZ, AWREJCEWICZ JAN Int. J. Bifurcation Chaos 21 2905 (2011)
  65. Chang Ch-M, Ge Zh-M Nonlinear Dyn 60 551 (2010)
  66. Ramírez R, Sadovskaia N Reports On Mathematical Physics 65 109 (2010)
  67. Dullin H R, Tsygvintsev A V 17 495 (2010)
  68. Fernandez O E, Mestdag T, Bloch A M Regul. Chaot. Dyn. 14 635 (2009)
  69. Borisov A V, Mamaev I S Regul. Chaot. Dyn. 13 443 (2008)
  70. Krechetnikov R, Marsden J E Rev. Mod. Phys. 79 519 (2007)
  71. Borisov A V, Kozlov V V, Mamaev I S Regul. Chaot. Dyn. 12 531 (2007)
  72. Borisov A V, Kilin A A, Mamaev I S Dokl. Phys. 51 272 (2006)
  73. Borisov A V, Mamaev I S Math Notes 77 855 (2005)
  74. Borisov A V, Borisov A V i dr Matem. Zametki 77 930 (2005)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions