Adiabatic invariants, diffusion and acceleration in rigid body dynamics

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• 作者：Alexey V. Borisov ; Ivan S. Mamaev
• 关键词：adiabatic invariants ; Liouville system ; transition through resonance ; adiabatic chaos
• 刊名：Regular and Chaotic Dynamics
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：21
• 期：2
• 页码：232-248
• 全文大小：777 KB
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• 作者单位：Alexey V. Borisov (1)
  Ivan S. Mamaev (1)
  
  1. Steklov Mathematical Institute, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Dynamical Systems and Ergodic Theory
  Russian Library of Science
  
• 出版者：MAIK Nauka/Interperiodica distributed exclusively by Springer Science+Business Media LLC.
• ISSN：1468-4845

文摘

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).