I am modelling a free damped simple pendulum and was wondering if anyone could refer me to a paper or perhaps provide me with an expression describing the motion of the pendlum with large initial amplitude. I have solved the equations numerically but am implementing an optimization routine and have been requested a closed form of the equations if possible to speed things up.(adsbygoogle = window.adsbygoogle || []).push({});

I have described the undamped case using elliptic integrals and jacobi functions and was wondering if there is some extension on this to include damping.

Equation to solve is

y'' + cy' -g/l siny = 0

Any help much appreciated!

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# Free damped pendulum solution : closed form

Can you offer guidance or do you also need help?

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