Jacobi Elliptic Functions and the Complete Solution to the Bead on the   Hoop Problem
  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. 
Thomas E. Baker and Andreas Bill
physics.class-ph