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The Chaotic Motion of a Rigid Body Rotating About a Fixed Point

  • F. El-Sabaa
  • M. El-Tarazi
Part of the NATO ASI Series book series (NSSB, volume 272)

Abstract

The dynamical system with two degrees of freedom has been studied by many authors. It is well known, that if the system possesses a first integral besides the integral of energy, then the system is completely integrable. After the fundamental works of Kolmogorov [1], Arnold [2] and Moser [3] (KAM) in 1960–1968, many theoretical and numerical results were presented by authors who treated the problem, when the system contained only the integral of energy (Jacobi’s integral). The results of (kam) have clarified the picture of nonintegrable systems through the small perturbations of integrable systems; for small perturbations we get very regular orbits, lying apparently on invariant tori, while for larger perturbations a part of the tori seems to be destroyed, and erratic orbits appear instead, filling the so-called stochastic region.

Keywords

Periodic Solution Periodic Orbit Rigid Body Periodic Motion Eulerian Angle 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Plenum Press, New York 1991

Authors and Affiliations

  • F. El-Sabaa
    • 1
  • M. El-Tarazi
    • 2
  1. 1.Department of Mathematics, Faculty of EducationAin Shamis UniversityCairoEgypt
  2. 2.Department of MathematicsKuwait UniversityKuwait

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