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Related Experiment Videos

Hannay's hoop beyond asymptotics.

Hwan Bae1, Norah Ali1, John F Lindner1

  • 1Physics Department, The College of Wooster, Wooster, Ohio 44691, USA.

Chaos (Woodbury, N.Y.)
|September 6, 2018
PubMed
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Geometric phase, or Hannay's angle, quantifies system anholonomy. This study explores classical geometric phase using a bead on a rotating hoop, extending theory to computational experiments.

Area of Science:

  • Classical mechanics
  • Geometric phase phenomena
  • Anholonomy in physical systems

Background:

  • Systems may not return to their initial state after traversing a closed path in parameter space.
  • This phenomenon, termed anholonomy, is quantified by geometric phase, known as Hannay's angle classically and Berry's phase quantum mechanically.
  • Understanding geometric phase is crucial in various physics domains.

Purpose of the Study:

  • To investigate the classical geometric phase (Hannay's angle) in a bead sliding on a rotating hoop.
  • To elucidate the roles of inertial and pseudo-forces in the bead's motion.
  • To computationally generalize the study of geometric phase beyond adiabatic approximations and bridge theory with experimental realization.

Main Methods:

  • Analyzing the dynamics of a bead on a frictionless rotating hoop.

Related Experiment Videos

  • Utilizing concepts from classical mechanics, including inertial and pseudo-forces.
  • Developing computational models to simulate the system's behavior for arbitrary motions.
  • Designing a physical experimental setup using sliding wet ice cylinders.

    • Main Results:

    • Demonstrated how forces in inertial and rotating frames influence the bead's trajectory.
    • Successfully generalized the computation of geometric phase for non-adiabatic motions.
    • Validated the theoretical framework through computational simulations.

    Conclusions:

    • The study successfully extends the understanding of classical geometric phase from theoretical concepts to practical, computationally-driven experiments.
    • The findings provide a foundation for experimental realization of geometric phase phenomena.
    • The research highlights the applicability of geometric phase concepts in classical mechanics and beyond.