[Tex/LaTex] Breaking long equation after a certain left bracket

bracketsequationsline-breaking

I am typing a long equation which needs to be broken just after the left bracket and three dots are placed at the end of the left bracket same line. Here is an example, in which, I need the third left bracket (i.e. of the column vector just before the plus sign) to be followed by three dots while aligning the rest of the equation in the newline with the equal sign.

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{center}
\begin{equation}\left[
  \begin{array}{c}
    \dot{\omega}_m \\
    \dot{\theta}_m \\
    \dot{\omega}_v \\
    \dot{I}_m \\
  \end{array}
\right]
=
\left[
  \begin{array}{cccc}
    -\frac{C_m}{J_m} & -\frac{P_s K_s \psi}{2 \pi r_s^2 J_m} & 0 & \frac{K_{tm}}{J_m} \\
    1 & 0 & 0 & 0 \\
    0 & -\frac{P_s K_s \mu_p R_{mp}}{2 \pi r_s J_v} & -\frac{C_v}{J_v} & 0 \\
    -\frac{K_{em}}{L_m} & 0 & 0 & -\frac{R_m}{L_m} \\
  \end{array}
\right]
\left[
  \begin{array}{c}
    \omega_m \\
    \theta_m \\
    \omega_v \\
    I_m \\
  \end{array}
\right]
+
\left[
  \begin{array}{cc}
    0 & 0 \\
    0 & 0 \\
    \frac{1}{J_v} & 0 \\
    0 & \frac{1}{L_m} \\
  \end{array}
\right]
\left[
  \begin{array}{c}
    F_v \\
    V_m(t) \\
  \end{array}
\right]
\end{equation}
\end{center}

\end{document}

Thanks in advance

Best Answer

It's not at all clear what you want to do; I would split the equation in this way

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation}
\begin{aligned}
  \begin{bmatrix}
    \dot{\omega}_m \\
    \dot{\theta}_m \\
    \dot{\omega}_v \\
    \dot{I}_m \\
  \end{bmatrix}
&=
  \begin{bmatrix}
    -\frac{C_m}{J_m} & -\frac{P_s K_s \psi}{2 \pi r_s^2 J_m} & 0 & \frac{K_{tm}}{J_m} \\
    1 & 0 & 0 & 0 \\
    0 & -\frac{P_s K_s \mu_p R_{mp}}{2 \pi r_s J_v} & -\frac{C_v}{J_v} & 0 \\
    -\frac{K_{em}}{L_m} & 0 & 0 & -\frac{R_m}{L_m} \\
  \end{bmatrix}
  \begin{bmatrix}
    \omega_m \\
    \theta_m \\
    \omega_v \\
    I_m \\
  \end{bmatrix}
\\
&\qquad+
  \begin{bmatrix}
    0 & 0 \\
    0 & 0 \\
    \frac{1}{J_v} & 0 \\
    0 & \frac{1}{L_m} \\
  \end{bmatrix}
  \begin{bmatrix}
    F_v \\
    V_m(t) \\
  \end{bmatrix}
\end{aligned}
\end{equation}

\end{document}

The center environment is out of place; the bmatrix environment gives better matrices than \left[\begin{array}{..}...\end{array}\right].

enter image description here

With a reduced column width one can try and squeeze the matrix columns and break at the product. Here's an example at a column width of 229.5pt (3.2 inches or 8 centimeters):

\documentclass[twocolumn]{article}
\usepackage{amsmath}
\begin{document}
\pagestyle{empty}

\begin{equation}
\setlength{\arraycolsep}{1pt}
\begin{aligned}
  \begin{bmatrix}
    \dot{\omega}_m \\
    \dot{\theta}_m \\
    \dot{\omega}_v \\
    \dot{I}_m \\
  \end{bmatrix}
&=
  \begin{bmatrix}
    -\frac{C_m}{J_m} & -\frac{P_s K_s \psi}{2 \pi r_s^2 J_m} & 0 & \frac{K_{tm}}{J_m} \\
    1 & 0 & 0 & 0 \\
    0 & -\frac{P_s K_s \mu_p R_{mp}}{2 \pi r_s J_v} & -\frac{C_v}{J_v} & 0 \\
    -\frac{K_{em}}{L_m} & 0 & 0 & -\frac{R_m}{L_m} \\
  \end{bmatrix}
\\
&\qquad\cdot
  \begin{bmatrix}
    \omega_m \\
    \theta_m \\
    \omega_v \\
    I_m \\
  \end{bmatrix}
+
  \begin{bmatrix}
    0 & 0 \\
    0 & 0 \\
    \frac{1}{J_v} & 0 \\
    0 & \frac{1}{L_m} \\
  \end{bmatrix}
  \begin{bmatrix}
    F_v \\
    V_m(t) \\
  \end{bmatrix}
\end{aligned}
\end{equation}
\end{document}

enter image description here

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