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Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 2012, Volume 12, Issue 2, Pages 90–95 (Mi isu301)  

Mechanics

Chaotic motion of top with displaced mass center

D. A. Losyakova

Samara State Aerospace University, Chair of Theoretical Mechanics

Abstract: The motion of solid body with a small displacement mass center from the axis of dynamic symmetry has been studied. Analytical conditions for the existence of a hyperbolic singular point in the phase portrait of the system and the analytical solution for the separatrices have been obtained. Body makes a chaotic motion near separatrices under the influence of small perturbations caused by the asymmetry of the body. Using the numerical simulation based on the Melnikov method in interpretation of Holmes–Marsden confirmation of the chaotic motion system has been received. This has been illustrated by a series of Poincare sections.

Key words: non-linear system, periodic perturbations, chaos, homoclinic orbits, Melnikov method, Poincare section.

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UDC: 531.36+534.1

Citation: D. A. Losyakova, “Chaotic motion of top with displaced mass center”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 12:2 (2012), 90–95

Citation in format AMSBIB
\Bibitem{Los12}
\by D.~A.~Losyakova
\paper Chaotic motion of top with displaced mass center
\jour Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform.
\yr 2012
\vol 12
\issue 2
\pages 90--95
\mathnet{http://mi.mathnet.ru/isu301}


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