Regular and Chaotic Dynamics

, Volume 14, Issue 2, pp 179–217 | Cite as

The Hamiltonian dynamics of self-gravitating liquid and gas ellipsoids

Research Articles

Abstract

The dynamics of self-gravitating liquid and gas ellipsoids is considered. A literary survey and authors’ original results obtained using modern techniques of nonlinear dynamics are presented. Strict Lagrangian and Hamiltonian formulations of the equations of motion are given; in particular, a Hamiltonian formalism based on Lie algebras is described. Problems related to nonintegrability and chaos are formulated and analyzed. All the known integrability cases are classified, and the most natural hypotheses on the nonintegrability of the equations of motion in the general case are presented. The results of numerical simulations are described. They, on the one hand, demonstrate a chaotic behavior of the system and, on the other hand, can in many cases serve as a numerical proof of the nonintegrability (the method of transversally intersecting separatrices).

Key words

liquid and gas self-gravitating ellipsoids integrability chaotic behavior 

MSC2000 numbers

70Hxx 

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© Pleiades Publishing, Ltd. 2009

Authors and Affiliations

  1. 1.Institute of Computer ScienceUdmurt State UniversityIzhevskRussia

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