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A. Belyakov, A.P. Seyranian:
"Twirling of hula-hoop: new results";
in: "Proceedings of the 7th European Nonlinear Dynamics Conference (ENOC 2011)", issued by: Universität Rom; Universität Rom ENOC2011, Rom, 2011, ISBN: 978-88-906234-2-4, 6 pages.

We consider twirling of a hula-hoop when the waist of a gymnast moves along an elliptic trajectory close to a circle. For the case of the circular trajectory, two families of exact solutions are obtained. Both of them correspond to twirling of the hula-hoop with a constant angular speed equal to the speed of the excitation. We show that one family of solutions is stable, while the other one is unstable. These exact solutions allow us to obtain approximate solutions for the case of an elliptic trajectory of the waist. We demonstrate that to twirl a hula-hoop one needs to rotate the waist with a phase difference lying between π/2 and π. An interesting effect of inverse twirling is described when the waist moves in a direction opposite to the hula-hoop rotation. The approximate analytical solutions are compared with the results of numerical simulation.

http://dx.doi.org/10.3267/ENOC2011Rome