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Geometrically modulated contact forces enable hula hoop levitation.

Xintong Zhu1, Olivia Pomerenk1, Leif Ristroph1

  • 1Applied Mathematics Laboratory, Courant Institute of Mathematical Sciences, Department of Mathematics, New York University, New York, NY 10012.

Proceedings of the National Academy of Sciences of the United States of America
|January 10, 2025
PubMed
Summary

Hula hooping is a form of mechanical levitation. Stable suspension requires specific body shapes and sufficient speed, revealing key physics of rolling objects on moving surfaces.

Keywords:
contact forcesdynamical systemsequilibrium and stabilityparametric excitationrigid-body dynamics

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Area of Science:

  • Physics
  • Mechanical Engineering
  • Robotics

Background:

  • Mechanical systems with moving contact points are prevalent in engineering and daily life.
  • Analyzing dynamic interactions between objects and complex moving surfaces, like in hula hooping, presents significant challenges.
  • Hula hooping is a familiar yet poorly understood example of dynamic object exploration on a moving structure.

Purpose of the Study:

  • To investigate hula hooping as a form of mechanical levitation against gravity.
  • To identify the conditions necessary for the stable suspension of an object rolling around a gyrating body.
  • To understand the interplay between object motion, body shape, and contact forces.

Main Methods:

  • Robotic experiments with hoops on various surface geometries.
  • Development of a mechanical model linking motion, shape, and contact forces.
  • Analysis of dimensionless factors to unify experimental observations.

Main Results:

  • In-plane hoop motion requires synchronization with body gyration, damping, and sufficient launching speed.
  • Vertical equilibrium is achieved with specific body shapes (e.g., 'hips' or critical slope).
  • Stability necessitates an hourglass shape with a 'waist' and exceeding critical curvature.

Conclusions:

  • The study reveals the fundamental mechanics of hula hoop levitation.
  • Geometric properties of the gyrating body are critical for stable suspension and equilibrium.
  • Findings offer strategies for motion control through geometry-based contact forces and prediction of equilibria.