13 Lyapunov functions
Now I will include friction in my problem: x¨ +sx˙ +sinx = 0, s > 0. I can rewrite my equation as the system x˙ = y, y˙ = −sy +sinx, which has the same equilibria as the conservative pendulum equation. Here, however, I can use the standard linearization approach to conclude that the origin is locally asymptotically stable (do this).
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