In this video, I find (and plot) the equations of motion for a pendulum using three different methods.
00:00 - Intro
01:21 - Newtonian
07:16 - Numerical solution (python)
14:49 - Lagrangian
22:46 - Hamiltonian
31:45 - Comparing Hamiltonian
36:05 - Phase space
Here are some links:
python code: https://trinket.io/glowscript/8df4807782
python code: https://trinket.io/glowscript/e750102850
Acceleration in polar coordinates https://youtu.be/EYPwDVANokc