English

Jacobi Elliptic Functions and the Complete Solution to the Bead on the Hoop Problem

Classical Physics 2012-05-23 v1

Abstract

Jacobi elliptic functions are flexible functions that appear in a variety of problems in physics and engineering. We introduce and describe important features of these functions and present a physical example from classical mechanics where they appear: a bead on a spinning hoop. We determine the complete analytical solution for the motion of a bead on the driven hoop for arbitrary initial conditions and parameter values.

Cite

@article{arxiv.1201.4201,
  title  = {Jacobi Elliptic Functions and the Complete Solution to the Bead on the Hoop Problem},
  author = {Thomas E. Baker and Andreas Bill},
  journal= {arXiv preprint arXiv:1201.4201},
  year   = {2012}
}

Comments

Accepted for publication in American Journal of Physics. 9 pages, 6 figures

R2 v1 2026-06-21T20:07:22.555Z