Аннотация:
In this paper, we consider the transition to chaos in the phase portrait of a restricted problem of rotation of a rigid body with a fixed point. Two interrelated mechanisms responsible for chaotization are indicated: (1) the growth of the homoclinic structure and (2) the development of cascades of period doubling bifurcations. On the zero level of the area integral, an adiabatic behavior of the system (as the energy tends to zero) is noted. Meander tori induced by the break of the torsion property of the mapping are found.
Ключевые слова:
motion of a rigid body, phase portrait, mechanism of chaotization, bifurcations.
Поступила в редакцию: 13.04.2007 Принята в печать: 28.10.2007
Образец цитирования:
A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Chaos in a Restricted Problem of Rotation of a Rigid Body with a Fixed Point”, Regul. Chaotic Dyn., 13:3 (2008), 221–233
\RBibitem{BorKilMam08}
\by A.~V.~Borisov, A.~A.~Kilin, I.~S.~Mamaev
\paper Chaos in a Restricted Problem of Rotation of a Rigid Body with a Fixed Point
\jour Regul. Chaotic Dyn.
\yr 2008
\vol 13
\issue 3
\pages 221--233
\mathnet{http://mi.mathnet.ru/rcd572}
\crossref{https://doi.org/10.1134/S1560354708030076}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2415375}
\zmath{https://zbmath.org/?q=an:1229.70011}
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd572
https://www.mathnet.ru/rus/rcd/v13/i3/p221
Эта публикация цитируется в следующих 3 статьяx:
E. V. Vetchanin, E. A. Mikishanina, “Vibrational Stability of Periodic Solutions of the Liouville Equations”, Rus. J. Nonlin. Dyn., 15:3 (2019), 351–363
Agnieszka Martens, “Test Rigid Bodies in Riemannian Spaces and Their Quantization”, Reports on Mathematical Physics, 71:3 (2013), 381
Manoj Srinivasan, “Chaos in a soda can: Non-periodic rocking of upright cylinders with sensitive dependence on initial conditions”, Mechanics Research Communications, 36:6 (2009), 722
Цитирование в формате AMSBIB
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