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 Nelin. Dinam.: Year: Volume: Issue: Page: Find

 Nelin. Dinam., 2005, Volume 1, Number 2, Pages 191–207 (Mi nd198)

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

A. V. Borisovab, A. A. Kilinba, I. S. Mamaevba

a Udmurt State University
b Institute of Computer Science

Abstract: The paper deals with a transition to chaos in the phase-plane portrait of a restricted problem of rotation of a rigid body with a fixed point. Two interrelated mechanisms responsible for chaotisation have been indicated: 1) growth of the homoclinic structure and 2) development of cascades of period doubling bifurcations. On the zero level of the integral of areas, an adiabatic behavior of the system (as the energy tends to zero) has been noticed. Meander tori induced by the breakdown of the torsion property of the mapping have been found.

Keywords: motion of a rigid body, phase-plane portrait, mechanism of chaotisation, bifurcations.

Full text: PDF file (703 kB)

Document Type: Article
UDC: 531.38

Citation: A. V. Borisov, A. A. Kilin, I. S. Mamaev, “Chaos in a restricted problem of rotation of a rigid body with a fixed point”, Nelin. Dinam., 1:2 (2005), 191–207

Citation in format AMSBIB
\Bibitem{BorKilMam05} \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 Nelin. Dinam. \yr 2005 \vol 1 \issue 2 \pages 191--207 \mathnet{http://mi.mathnet.ru/nd198}