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Regular and Chaotic Dynamics

, Volume 13, Issue 3, pp 221–233 | Cite as

Chaos in a restricted problem of rotation of a rigid body with a fixed point

  • A. V. Borisov
  • A. A. Kilin
  • I. S. Mamaev
Research Articles

Abstract

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.

Key words

motion of a rigid body phase portrait mechanism of chaotization bifurcations 

MSC2000 numbers

70E17 65P30 83C10 

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Copyright information

© MAIK Nauka 2008

Authors and Affiliations

  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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