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Regular and Chaotic Dynamics

, Volume 21, Issue 2, pp 232–248 | Cite as

Adiabatic invariants, diffusion and acceleration in rigid body dynamics

  • Alexey V. Borisov
  • Ivan S. Mamaev
Article

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 

MSC2010 numbers

70F15 37J30 37M25 

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© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia

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