I'm trying to find the equilibrium points of a nonlinear model where input u=u* <1 is constant. T and $\zeta$ are given.
$\dot{x}_1 = x_2\qquad\qquad\qquad\qquad\qquad$ (1)
$\dot{x}_2 = -x_1-2\zeta x_2+\frac{1}{3}x_3^2\qquad\qquad$ (2)
$\dot{x}_3 = \frac{1}{T}[-(1-x_1)x_3+\frac{2}{3}u]\qquad\quad$ (3)
With previous problems, where input u wasn't a part of the model, all I've had to do was set $\dot{x}_1,\dot{x}_2,\dot{x}_3 = 0$ and calculate $x_1,x_2,x_3$. However now I'm unsure of how to start. What I've tried is to set $x_2=0$, in (2) define $x_1$ in terms of $x_3$, and put that in (3) to try and break out $x_3$. Then I get $x_3^3-3x_3+2u=0$ and from here I don't know how to advance since u is not defined and I get a really long expression for $x_3$.
Am I doing this completely wrong? Would really appreciate some help with this problem.