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Here are some examples of equations.

\begin{eqnarray}
L &=& 2 \pi \rho a_0 b U \left( U \theta - \dot{h} + (\frac{a_0}{2}
- a_1) \dot{\theta} \right) C(i \omega) \nonumber \\ &+& \pi \rho
a_0^2 b \left( U \dot{\theta} - \ddot{h} - a_1 \ddot{\theta} \right)
\label{Lift1.eq}
\end{eqnarray}

That one was nice, but these are better.

\begin{eqnarray}
\dot{\phi} &=& \psi_2 + g_1 \theta + h_3 v, \label{newstate1.eq} \\
\dot{\psi_2} &=& -g_0 \psi_2 + g_2 \theta - C_f sign(\dot{\phi}), \label{newstate2.eq} \\
\dot{\theta} &=& v \label{newstate3.eq}
\end{eqnarray}

Oh, and don't forget...

\begin{eqnarray}
\dot{V}(x) &=& \phi \psi_2 + g_1 \phi \theta + h_3 \phi v - g_0
\psi_2^2 + g_2 \psi_2 \theta + m \theta v
\nonumber \\
&=& \left[
\begin{matrix}
    \phi \\
    \psi_2 \\
    \theta
\end{matrix}
\right]^T \left[
\begin{matrix}
    0 & 1/2 & g_1/2 \\
    1/2 & -g_0 & g_2/2 \\
    g_1/2 & g_2/2 & 0
\end{matrix}
\right] \left[
\begin{matrix}
    \phi \\
    \psi_2 \\
    \theta
\end{matrix}
\right] + \left[
\begin{matrix}
    \ h_3 \ 0 \ m
\end{matrix}
\right]\left[
\begin{matrix}
    \phi \\
    \psi_2 \\
    \theta
\end{matrix}
\right] v \label{derivlyap2.eq}
\end{eqnarray}

which is a Lyapunov equation. This next one is my favorite.

\begin{equation}
v = \left\{ \begin{array} {ccl} \left( c_0 + \frac{a + \sqrt{a^2 +
b^2}}{b} \right) b & \mbox{ if } & \gamma\neq 0\cr 0 &  \mbox{ if }
& \gamma=0 \end{array}\right. , \label{vcontrol.eq}
\end{equation}

And finally,

\begin{eqnarray}
\left[ \begin{matrix}
    \dot{\phi} \\
    \ddot{\phi}
\end{matrix} \right]
&=& \left[ \begin{matrix}
    0 &\ 1 \\
    0 &\ -b_a / J_a
\end{matrix} \right]
\left[ \begin{matrix}
    \phi \\
    \dot{\phi}
\end{matrix} \right]
+ \left[ \begin{matrix}
    0 \\
    l / J_a
\end{matrix} \right] N \nonumber\\
y &=& \left[ \begin{matrix}
    1 \ 0
\end{matrix} \right]
\left[ \begin{matrix}
    \phi \\
    \dot{\phi}
\end{matrix} \right]
+ \left[ \begin{matrix}
    0
\end{matrix} \right] N
\label{continss.eq}
\end{eqnarray}

This is how you would reference a particular equation, say
\eqref{derivlyap2.eq}, in the text. This is how you would write math
in the text, $E = m c^2$.

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