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.
Citation:
Alexey V. Borisov, Ivan S. Mamaev, “Adiabatic Invariants, Diffusion and Acceleration in Rigid Body Dynamics”, Regul. Chaotic Dyn., 21:2 (2016), 232–248
\Bibitem{BorMam16}
\by Alexey V. Borisov, Ivan S. Mamaev
\paper Adiabatic Invariants, Diffusion and Acceleration in Rigid Body Dynamics
\jour Regul. Chaotic Dyn.
\yr 2016
\vol 21
\issue 2
\pages 232--248
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\crossref{https://doi.org/10.1134/S1560354716020064}
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Linking options:
https://www.mathnet.ru/eng/rcd59
https://www.mathnet.ru/eng/rcd/v21/i2/p232
This publication is cited in the following 4 articles:
J. Bao, A. Neishtadt, “Separatrix crossing in rotation of a body with changing geometry of masses”, SIAM J. Appl. Dyn. Syst., 18:1 (2019), 150–171
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
V. S. Aslanov, “Exact solutions and adiabatic invariants for equations of satellite attitude motion under Coulomb torque”, Nonlinear Dyn., 90:4 (2017), 2545–2556
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
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