Analytic solution to the pendulum equation for a given initial conditions

Analytic solution to the pendulum equation for a given initial conditions

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In this paper we give the analytical solution for the undamped pendulum equation for a given arbitrary initial conditions.This solution is expressed in terms of the Jacobian elliptic dietrich scissors functions.Approximated trigonometric solution is also provided.Three practical formulas for the period of oscillations are given.The pioneer ddj sz dimensions results are illustrated with examples.

Keywords: Undamped pendulum, Duffing equation, Period of oscillations, Jacobian elliptic functions.