[lagrange77]

> It models first order perturbations over a stable equilibrium. For sufficiently small perturbations around a stable equilibrium everything is an harmonic oscillator.

That's the same reason, why we linearize nonlinear systems around the equilibria to apply linear control theory, right?

While in control, this makes sense to me, since the goal is often to stabilize the system, how does this help with modeling the whole system in general (far away from any equilibrium point)?

[pa7x1]

Yes, near a stable equilibrium you can always linearize a system to model its behavior quite accurately for small perturbations. That's the crux of what it was pointed above.

Outside of equilibrium things get more complicated. In principle, you can still do a first order expansion to understand the dynamics in a vicinity of that regime, the problem is that outside equilibrium you are not going to stay near the point of the solution space you started at. You will keep drifting, at least until you reach another stable equilibrium if there is one.

Systems outside equilibrium are much harder to study because we cannot linearize. Basically.