Reading through my notes in dynamical systems. I get to a point where it asks to write the Van der Poll equation as the state space form.

$\ddot \theta - \mu (1 - \theta^2) \dot \theta + \theta = 0$


$x_1 = \theta$ and $x_2 = \dot x_1$


$\dot x_1 = x_2$

$\dot x_2 = -x_1 - \mu x_2 x_1^2 + \mu x_2$

But because of the second term of $\dot x_2$ I don't know how to put it in state space form since it is a non-linear term. Any advise on how to do it? Is there a way to linearize this system?

  • 2
    $\begingroup$ State space form doesn't have to be linear. You have completely answered the question. $\endgroup$ Dec 30, 2013 at 18:38

1 Answer 1


It is in state space form. What you are looking for is the "matrix form" and this is not possible since the system is non-linear.

Recall in the state space form, the left hand side should only have derivatives of the state, and the right hand side should have only constants, and functions of time (including external inputs)


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