The Dynamics of a Bead Sliding on a Freely Rotating Horizontal Wire: An Analytical Solution

This paper analyzes the dynamics of a bead sliding along a rotating horizontal wire whose rate of rotation varies due to the motion of the bead. Legendre’s elliptic integrals are used to obtain an analytical solution of the equation of motion given by a nonlinear second-order differential equation. The analytical solution is used to determine the terminal velocity of the bead and the asymptotic angle of the wire.