Long matrix equation splitting

Question

I am trying to write a long equation which includes a long matrix. I have tried many solutions (multiline, split) from the other so answers but the problem still exists. Could you help me to find out the problem? Thank you in advance.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}

\begin{document}

\begin{equation}
\begin{multiline}
\label{nineth}
\begin{bmatrix}
\dot{x}\\
\dot{y}\\
\dot{z}\\
\end{bmatrix} =
\begin{bmatrix}
R_{0}^{0} \begin{bmatrix}
0\\ 0\\ 1 
\end{bmatrix} x
(d^{0}_{5}-d^{0}_{0}) & 
R^{0}_{1} \begin{bmatrix}
0\\ 0\\ 1 
\end{bmatrix} x
(d^{0}_{5}-d^{0}_{1}) & 
R^{0}_{2} \begin{bmatrix}
0\\ 0\\ 1 
\end{bmatrix} x
(d^{0}_{5}-d^{0}_{2}) & 
R^{0}_{3} \begin{bmatrix}
0\\ 0\\ 1 
\end{bmatrix} x
(d^{0}_{5}-d^{0}_{3}) & \\
R^{0}_{4} \begin{bmatrix}
0\\ 0\\ 1  
\end{bmatrix} x
(d^{0}_{5}-d^{0}_{4}) &
\end{bmatrix}
\begin{bmatrix}
\dot{\theta_{1}} \\
\dot{\theta_{2}} \\
\dot{\theta_{3}} \\
\dot{\theta_{4}} \\
\dot{\theta_{5}} \\
\end{bmatrix}
\end{multiline}
\end{equation}
\end{document}

As you can see there are 3 terms in the equation, 2nd term should be splitted but the result of the code is wrong in the image.

Answer 1

I'm not sure that the matrix form is really helpful for your readers; in this case a summation seems much better:

\documentclass{article}
\usepackage{amsmath}

\begin{document}

\begin{equation}
\begin{bmatrix} \dot{x} \\ \dot{y} \\ \dot{z} \end{bmatrix} -
\sum_{k=0}^4 R^{0}_{k}
             \begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix}
             x(d^{0}_{5}-d^{0}_{k}) \dot{\theta}_{k+1}
\end{equation}

\end{document}

Alternatively,

\begin{equation}
\begin{bmatrix} \dot{x} \\ \dot{y} \\ \dot{z} \end{bmatrix} -
\begin{bmatrix} S_0 & S_1 & S_2 & S_3 & S_4 \end{bmatrix}
\begin{bmatrix}
  \dot{\theta}_1 \\ \dot{\theta}_2 \\ \dot{\theta}_3 \\ \dot{\theta}_4 \\ \dot{\theta}_5
\end{bmatrix},
\qquad S_k=R^{0}_{k}\begin{bmatrix} 0 \\ 0 \\ 1 \end{bmatrix}x(d^{0}_{5}-d^{0}_{k})
\end{equation}

Answer 2

I propose to use multlined environment (from mathtools) inside the large matrix, and the geometry package to have more decent margins by default.

Unrelated: needless to load inputenc with option [utf8] nowadays (unless you have an old version of LaTeX), nor amsfonts if you load amssymb – the latter does it for you.

\documentclass{article}
\usepackage{geometry}
\usepackage{mathtools}
\usepackage{amssymb}
\usepackage{bigstrut}
\setlength{\bigstrutjot}{1ex}

\begin{document}

\begin{equation}
\label{nineth}
 \begin{bmatrix}
\dot{x}\bigstrut[t]\\
\dot{y}\\
\dot{z}\bigstrut[b]
\end{bmatrix} =
\begin{bmatrix}
\begin{multlined}
R_{0}^{0} \begin{bmatrix}
0\\ 0\\ 1
\end{bmatrix} x
(d^{0}_{5}-d^{0}_{0}) \quad
R^{0}_{1} \begin{bmatrix}
0\\ 0\\ 1
\end{bmatrix} x
(d^{0}_{5}-d^{0}_{1})\quad
R^{0}_{2} \begin{bmatrix}
0\\ 0\\ 1
\end{bmatrix} x
(d^{0}_{5}-d^{0}_{2})\\[-2ex]
R^{0}_{3} \begin{bmatrix}
0\\ 0\\ 1
\end{bmatrix} x
(d^{0}_{5}-d^{0}_{3}) \quad
R^{0}_{4} \begin{bmatrix}
0\\ 0\\ 1
\end{bmatrix} x
(d^{0}_{5}-d^{0}_{4})
\end{multlined}
\end{bmatrix}
\begin{bmatrix}
\dot{\theta_{1}}\bigstrut[t] \\[0.5ex]
\dot{\theta_{2}} \\[0.5ex]
\dot{\theta_{3}} \\[0.5ex]
\dot{\theta_{4}} \\[0.5ex]
\dot{\theta_{5}}\bigstrut[b]
\end{bmatrix}
\end{equation}

\end{document}