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Regul. Chaotic Dyn., 2016, Volume 21, Issue 2, Pages 232–248 (Mi rcd59)  
This article is cited in 3 scientific papers (total in 3 papers)

Adiabatic Invariants, Diffusion and Acceleration in Rigid Body Dynamics

Alexey V. Borisov, Ivan S. Mamaev

Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

Abstract: The onset of adiabatic chaos in rigid body dynamics is considered. A comparison of the analytically calculated diffusion coefficient describing probabilistic effects in the zone of chaos with a numerical experiment is made. An analysis of the splitting of asymptotic surfaces is performed and uncertainty curves are constructed in the Poincaré – Zhukovsky problem. The application of Hamiltonian methods to nonholonomic systems is discussed. New problem statements are given which are related to the destruction of an adiabatic invariant and to the acceleration of the system (Fermi’s acceleration).

Keywords: adiabatic invariants, Liouville system, transition through resonance, adiabatic chaos

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Scientific Foundation (project No. 14-50-00005).


DOI: https://doi.org/10.1134/S1560354716020064

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 70F15, 37J30, 37M25
Received: 12.12.2015
Language: English

Citation: Alexey V. Borisov, Ivan S. Mamaev, “Adiabatic Invariants, Diffusion and Acceleration in Rigid Body Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 232–248

Citation in format AMSBIB
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\vol 21
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\pages 232--248
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Pavel E. Ryabov, Andrej A. Oshemkov, Sergei V. Sokolov, “The Integrable Case of Adler – van Moerbeke. Discriminant Set and Bifurcation Diagram”, Regul. Chaotic Dyn., 21:5 (2016), 581–592  mathnet  crossref  mathscinet  zmath
    2. A. V. Borisov, I. S. Mamaev, I. A. Bizyaev, “Dynamical systems with non-integrable constraints, vakonomic mechanics, sub-Riemannian geometry, and non-holonomic mechanics”, Russian Math. Surveys, 72:5 (2017), 783–840  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. V. S. Aslanov, “Exact solutions and adiabatic invariants for equations of satellite attitude motion under Coulomb torque”, Nonlinear Dyn., 90:4 (2017), 2545–2556  crossref  isi  scopus
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