The explicit Euler scheme
Here we can see the calculations obtained with the explicit scheme. The initial conditions are q0=p, wi=0 :
We can see that the results are quite dependant of the time step. Indeed, with Dt=0.1, the calculation diverges. Whereas with Dt=0.01, quite good results are generally obtained.
Nevertheless, with a damped pendulum there is no divergence. This is due, of course, to the viscous effects.