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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:
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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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http://mi.mathnet.ru/eng/rcd59 http://mi.mathnet.ru/eng/rcd/v21/i2/p232
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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
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V. S. Aslanov, “Exact solutions and adiabatic invariants for equations of satellite attitude motion under Coulomb torque”, Nonlinear Dyn., 90:4 (2017), 2545–2556
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