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

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.

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

References in corpus (1)

• Bead, Hoop, and Spring as a Classical Spontaneous Symmetry Breaking Problem

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