In my notes on non-linear linearization there is the following example. It asks to verify the solution to the state-space equation. My understanding is that the solution is where the equilibrium point is. In other words, where the vector x'(t) is equal to zero. Thus, I plugged in the solution into x'(t) and one can see that it is not zero. Specifically, for the theta'(t) term, it is equal to omega_0 which is clearly not zero. Or have I misunderstood these notes?
