INTEGRABLE EULER TOP AND NONHOLONOMIC CHAPLYGIN BALL

被引：21
|
作者：
Tsiganov, Andrey [1 ]
机构：
[1] St Petersburg State Univ, St Petersburg, Russia
来源：
JOURNAL OF GEOMETRIC MECHANICS | 2011年 / 3卷 / 03期
关键词：
Integrable nonholonomic systems; bi-Hamiltonian geometry; SEPARATION; VARIABLES; SYSTEMS; MOTION; BODY;
D O I：
10.3934/jgm.2011.3.337
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We discuss the Poisson structures, Lax matrices, r-matrices, bi-hamiltonian structures, the variables of separation and other attributes of the modern theory of dynamical systems in application to the integrable Euler top and to the nonholonomic Chaplygin ball.
引用
收藏
页码：337 / 362
页数：26
相关论文
共 50 条
  • [1] Integrable Discretization and Deformation of the Nonholonomic Chaplygin Ball
    Tsiganov, Andrey V.
    REGULAR & CHAOTIC DYNAMICS, 2017, 22 (04): : 353 - 367
  • [2] Integrable discretization and deformation of the nonholonomic Chaplygin ball
    Andrey V. Tsiganov
    Regular and Chaotic Dynamics, 2017, 22 : 353 - 367
  • [3] Nonintegrability and obstructions to the hamiltonianization of a nonholonomic Chaplygin top
    Bizyaev, I. A.
    DOKLADY MATHEMATICS, 2014, 90 (02) : 631 - 634
  • [4] Spiral chaos in the nonholonomic model of a Chaplygin top
    Alexey V. Borisov
    Alexey O. Kazakov
    Igor R. Sataev
    Regular and Chaotic Dynamics, 2016, 21 : 939 - 954
  • [5] Nonintegrability and obstructions to the hamiltonianization of a nonholonomic Chaplygin top
    I. A. Bizyaev
    Doklady Mathematics, 2014, 90 : 631 - 634
  • [6] Spiral Chaos in the Nonholonomic Model of a Chaplygin Top
    Borisov, Alexey V.
    Kazakov, Alexey O.
    Sataev, Igor R.
    REGULAR & CHAOTIC DYNAMICS, 2016, 21 (7-8): : 939 - 954
  • [7] Integrable discretizations of the Euler top
    Bobenko, AI
    Lorbeer, B
    Suris, YB
    JOURNAL OF MATHEMATICAL PHYSICS, 1998, 39 (12) : 6668 - 6683
  • [8] Nonholonomic Noetherian Symmetries and Integrals of the Routh Sphere and the Chaplygin Ball
    Bustamante, Miguel D.
    Lynch, Peter
    REGULAR & CHAOTIC DYNAMICS, 2019, 24 (05): : 511 - 524
  • [9] Nonholonomic Noetherian Symmetries and Integrals of the Routh Sphere and the Chaplygin Ball
    Miguel D. Bustamante
    Peter Lynch
    Regular and Chaotic Dynamics, 2019, 24 : 511 - 524
  • [10] The reversal and chaotic attractor in the nonholonomic model of Chaplygin’s top
    Alexey V. Borisov
    Alexey O. Kazakov
    Igor R. Sataev
    Regular and Chaotic Dynamics, 2014, 19 : 718 - 733
12345