Mathematically model a hula hoop, being driven to hypocycloidal motion by a moving waist. This should be (relatively) easy.
Next, model a flexible hula hoop that deforms like an ellipse under centrifugal force. I predict getting such a hula hoop started into motion is difficult, as the resonant frequency keeps changing due to elongation. Or energy gets dissipated due to to bending and unbending.
HT Emma
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