Analytic solution to the pendulum equation for a given initial conditions

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 functions. Approximated trigonometric solution is also provided. Three practical formulas for the period of oscillat...

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Veröffentlicht in:	Journal of King Saud University. Science 2020-01, Vol.32 (1), p.974-978
1. Verfasser:	Salas S., Alvaro H.
Format:	Artikel
Sprache:	eng
Schlagworte:	Duffing equation Jacobian elliptic functions Period of oscillations Undamped pendulum
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Zusammenfassung:	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 functions. Approximated trigonometric solution is also provided. Three practical formulas for the period of oscillations are given. The results are illustrated with examples.
ISSN:	1018-3647
DOI:	10.1016/j.jksus.2019.07.005