View source for Errata: In Example 2.1, the state space equations for the balance system are missing a divisor of J t in one of the terms

{{errata page
| chapter = System Modeling
| page = 37
| line = 4
| contributor = C. Bray
| date = 27 Apr 2010; A. Tits, 4 Sep 2010
| rev = 2.10c
| version = Third printing
| text = 
In the state space equations for the balance systems example, the numerator of the equation for <amsmath>d\dot{p}/dt</amsmath> is missing a divisor of <math>J_t</math> in the <math>\gamma</math> term.  The correct equation is
<center><amsmath>
    \frac{d}{dt}\begin{bmatrix} p \\ \theta \\ \dot p \\ \dot \theta \end{bmatrix} =
    \begin{bmatrix} \dot p \\ \dot \theta \\
      \dfrac{
        - m l s_\theta \dot\theta^2 
        + m g (m l^2 / J_t) s_\theta c_\theta 
	- c \dot p - (\gamma/J_t) m l c_\theta \dot\theta
        + u}
        {M_t - m (m l^2 / J_t) c_\theta^2  } \\[2ex]
      \dfrac{
	- m l^2 s_\theta c_\theta \dot\theta^2 
        + M_t g l s_\theta 
        - c l c_\theta \dot p - \gamma (M_t/m) \dot \theta
	+ l c_\theta u}
        {J_t (M_t/m) - m (l c_\theta)^2}
    \end{bmatrix}.
</amsmath></center>
This error propagates to the next equation, where the <math>J_t</math> term in the (3,4) entry of the dynamics matrix should be deleted.  The correct expression is
<center><amsmath>
    \frac{d}{dt}\begin{bmatrix} p \\ \theta \\ \dot p \\ \dot \theta \end{bmatrix} =
    \begin{bmatrix}
      0 & 0 & 1 & 0 \\
      0 & 0 & 0 & 1 \\[0.5ex]
      0 & {m^2 l^2 g}/{\mu}
        & {-c J_t}/{\mu} 
	& {-\gamma l m}/{\mu} \\[0.5ex]
      0 & {M_t m g l}/{\mu}
        & {-c l m}/{\mu}
        & {-\gamma M_t}/{\mu}
    \end{bmatrix} \begin{bmatrix} p \\ \theta \\ \dot p \\ \dot \theta \end{bmatrix} + 
    \begin{bmatrix}
      0 \\ 0 \\[0.5ex]
        {J_t}/{\mu} \\[0.5ex] 
        {l m}/{\mu} 
    \end{bmatrix} u
</amsmath></center>
}}