How to write matrix in equation environment?

I'm using LaTeX to write my paper and every equation needs to be numbered, so I use the equation environment. However, it fails to compile.

\documentclass[UTF8]{ctexart}
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{graphicx}
\usepackage{epstopdf}
\begin{document}
\begin{equation}
$\begin{bmatrix} L_{a1} & 0 \\ 0 & L_{a2} \end{bmatrix} \begin{bmatrix} I_{a1} \\ I_{a2} \end{bmatrix} + \begin{bmatrix} R_{a1} & 0 \\ 0 & R_{a2} \end{bmatrix} \begin{bmatrix} I_{a1} \\ I_{a2} \end{bmatrix} + \begin{bmatrix} K_{e1} & 0 \\ 0 & K_{e2} \end{bmatrix} \begin{bmatrix} theta_1 \\ theta_2 \end{bmatrix} = \begin{bmatrix} V_{a1} \\ V_{a2} \end{bmatrix}$
\end{equation}
\end{document}

So my question is: how to revise it? In addtion, I would like to know why the math expression that follows is wrong:

$$B = \frac{J_2}{N_1 N_2}+\frac{m_2 r_2^2}{4 N_1 N_2}+\frac{m_2 r_1 r_2}{2 N_1 N_2} cos(\frac{\theat_{m2}}{N_2})$$
$$C = \frac{-m_2 r_1 r_2}{N_1 N_2}(\frac{\theat_{m1} \theat_{m2}}{N_1}+\frac{\theat_{m2}^2}{2 N_2}) sin\frac{\theat_{m2}}{N_2}$$
$$D = J_{m1} +\frac{J_2}{N_2^2}+\frac{m_2 r_2^2}{4 N_2^2}$$
$$E = \frac{J_2}{N_1 N_2}+\frac{m_2 r_2^2}{4 N_1 N_2}+\frac{m_2 r_1 r_2}{2 N_1 N_2} cos(\frac{\theat_{m2}}{N_2})$$

LaTeX gives the information:

Undefined control sequence. [..._2}{2 N_1 N_2} cos(\frac{\theat_{m2}}{N_2}]
• \theta not \theat. Also you don't need  inside equation environment. – Sigur Jan 7 '14 at 15:44