Closed form integration of the rotating plane pendulum nonlinear equation

Abstract

The article deals with the nonlinear differential equation of the frictionless motion of a heavy pendulum swinging in a vertical plane which rotates at a fixed angular speed. The authors focused on its closed form integration by means of the Jacobi elliptic functions. This research took its origin by an autonomous work of the authors; this subject was also developed by [3], who did a treatment by far different from ours.