Dynamics of Hula-Hoop in Horizontal Plane: Periodic Solutions and Chaos

Dynamics of Hula-Hoop in Horizontal Plane: Periodic Solutions and Chaos

The motions of hula-hoop were widely analyzed about the non-dimensional parameters related to damping and vibration amplitude of fulcrum using ordinary numerical integration and the shooting method. There exist many types of motion depending on the damping and the amplitude of fulcrum, namely, symme...

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Veröffentlicht in:TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C 2005/07/25, Vol.71(707), pp.2172-2179
Hauptverfasser: YOSHITAKE, Yutaka, HARADA, Akira, FUKUSHIMA, Akizumi, SAKAGUCHI, Kinya, ISHIBASHI, Tsukasa
Format: Artikel
Sprache:eng ; jpn
Schlagworte:
Bifurcation
Chaos
Hula-Hoop
Nonlinear Vibration
Shooting Method
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container_end_page 2179
container_issue 707
container_start_page 2172
container_title TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series C
container_volume 71
creator YOSHITAKE, Yutaka
HARADA, Akira
FUKUSHIMA, Akizumi
SAKAGUCHI, Kinya
ISHIBASHI, Tsukasa
description The motions of hula-hoop were widely analyzed about the non-dimensional parameters related to damping and vibration amplitude of fulcrum using ordinary numerical integration and the shooting method. There exist many types of motion depending on the damping and the amplitude of fulcrum, namely, symmetrical and unsymmetrical rotation, symmetrical and unsymmetrical subharmonic vibration, rotation superior and vibration superior type chaos and so on. It is made clear that each periodic solution bifurcates from symmetrical motion to unsymmetrical motion, and bifurcates to chaos after period doubling bifurcations. The obtained solutions were verified by the experiment, and the results were qualitatively in good agreement with each other. Lastly, the motions of hula-hoop were evaluated from the viewpoint of the kinetic energy of the hula-hoop.
doi_str_mv 10.1299/kikaic.71.2172
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source J-STAGE Free; Elektronische Zeitschriftenbibliothek - Frei zugängliche E-Journals
subjects Bifurcation
Chaos
Hula-Hoop
Nonlinear Vibration
Shooting Method
title Dynamics of Hula-Hoop in Horizontal Plane: Periodic Solutions and Chaos
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