Geometrically modulated contact forces enable hula hoop levitation

• 成果类型: Article
• 署名作者: Zhu, Xintong; Pomerenk, Olivia; Ristroph, Leif
• 署名单位: New York University
• 刊物名称: PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
• ISSN/ISSBN: 0027-12503
• DOI: 10.1073/pnas.2411588121
• 发表日期: 2025-01-07
• 关键词: dynamics; flight; STABILITY

摘要

Mechanical systems with moving points of contact-including rolling, sliding, and impacts-are common in engineering applications and everyday experiences. The challenges in analyzing such systems are compounded when an object dynamically explores the complex surface shape of a moving structure, as arises in familiar but poorly understood contexts such as hula hooping. We study this activity as a unique form of mechanical levitation against gravity and identify the conditions required for the stable suspension of an object rolling around a gyrating body. We combine robotic experiments involving hoops twirling on surfaces of various geometries and a model that links the motions and shape to the contact forces generated. The in-plane motions of the hoop involve synchronization to the body gyration that is shown to require damping and sufficiently high launching speed. Further, vertical equilibrium is achieved only for bodies with hips or a critical slope of the surface, while stability requires an hourglass shape with a waist and whose curvature exceeds a critical value. Analysis of the model reveals dimensionless factors that successfully organize and unify observations across a wide range of geometries and kinematics. By revealing and explaining the mechanics of hula hoop levitation, these results motivate strategies for motion control via geometry-dependent contact forces and for accurately predicting the resulting equilibria and their stability.