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!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Free damped pendulum solution : closed form

Can you offer guidance or do you also need help?

Draft saved
Draft deleted

**Physics Forums | Science Articles, Homework Help, Discussion**