How can long formulas be written more beautifully?

Question

How do you write a long formula in a more beautiful manner

1. for the better, all my formulas in lines with the same length.
2. formulas are long with slightly smaller text.
3. Is it better to be done automatically (because I have a lot of formulas).

I was was wondering that how formulas in the books are so pretty? How are they written?

For example, I put some of my equations below:

\documentclass{article}
\usepackage[fleqn]{amsmath}
\usepackage{amsthm}
\usepackage{amssymb}
\usepackage{breqn}
\title{‏break a long formulation}
\author{}
\begin{document}
\maketitle
It was wandering that how formula in book are very pretty? how they write?
\begin{align*}
&\left( \hat{E}h+2{{E}^{s}} \right)\,\left[ \sum\limits_{m=1}^{{{N}_{x}}}{B_{im}^{x}}{{u}_{mj}}+\left( \sum\limits_{m=1}^{{{N}_{x}}}{A_{im}^{x}}{{w}_{mj}} \right)\left( \sum\limits_{m=1}^{{{N}_{x}}}{B_{im}^{x}}{{w}_{mj}} \right) \right]+\\
&\left[ \nu \hat{E}h+Gh+2{{E}^{s}} \right]\,\left[ \sum\limits_{m=1}^{{{N}_{x}}}{\sum\limits_{n=1}^{{{N}_{y}}}{A_{im}^{x}A_{jn}^{y}{{v}_{mn}}}} \right.+\left( \sum\limits_{n=1}^{{{N}_{y}}}{A_{jn}^{y}}{{w}_{in}} \right).\\
&\left. \left( \sum\limits_{m=1}^{{{N}_{x}}}{\sum\limits_{n=1}^{{{N}_{y}}}{A_{im}^{x}A_{jn}^{y}{{w}_{mn}}}} \right) \right]\left[ Gh+2\left( \left. 2{{\mu }^{s}}-{{\tau }^{s}} \right) \right. \right]\left[ \sum\limits_{n=1}^{{{N}_{y}}}{B_{jn}^{y}{{u}_{in}}} \right.+\\
&\left. \left( \sum\limits_{m=1}^{{{N}_{x}}}{A_{im}^{x}}{{w}_{mj}} \right)\left( \sum\limits_{n=1}^{{{N}_{y}}}{B_{jn}^{y}{{w}_{in}}} \right) \right]=\rho h{{\ddot{u}}_{ij}}-\mu \rho h\left( \sum\limits_{m=1}^{{{N}_{x}}}{B_{im}^{x}}{{{\ddot{u}}}_{mj}} \right.+\\
&\left. \sum\limits_{n=1}^{{{N}_{y}}}{B_{jn}^{y}}{{{\ddot{u}}}_{in}} \right)\\     
\end{align*}

\begin{dmath}
\left( \hat{E}h+2{{E}^{s}} \right)\left[ \sum\limits_{n=1}^{{{N}_{y}}}{B_{jn}^{y}{{v}_{in}}}+\left( \sum\limits_{n=1}^{{{N}_{y}}}{A_{jn}^{y}{{w}_{in}}} \right)\left( \sum\limits_{n=1}^{{{N}_{y}}}{B_{jn}^{y}{{w}_{in}}} \right) \right]+\left( \nu \hat{E}h+Gh+2{{E}^{s}} \right)\left[ \sum\limits_{m=1}^{{{N}_{x}}}{\sum\limits_{n=1}^{{{N}_{y}}}{A_{im}^{x}A_{jn}^{y}{{u}_{mn}}}} \right.+\left( \sum\limits_{m=1}^{{{N}_{x}}}{A_{im}^{x}}{{w}_{mj}} \right)\left( \sum\limits_{m=1}^{{{N}_{x}}}{\sum\limits_{n=1}^{{{N}_{y}}}{A_{im}^{x}A_{jn}^{y}{{w}_{mn}}}} \right)+\left[ Gh \right.+\left. 2\left( 2{{\mu }^{s}}-{{\tau }^{s}} \right) \right]\left[ \sum\limits_{m=1}^{{{N}_{x}}}{B_{im}^{x}}{{v}_{mj}}+ \right. \left. \left( \sum\limits_{n=1}^{{{N}_{y}}}{A_{jn}^{y}}{{w}_{in}} \right)\left( \sum\limits_{m=1}^{{{N}_{x}}}{B_{im}^{x}}{{w}_{mj}} \right) \right]=\rho h{{\ddot{v}}_{ij}}-\mu \rho h\left( \sum\limits_{m=1}^{{{N}_{x}}}{B_{im}^{x}}{{{\ddot{v}}}_{mj}} \right.+ \left. +\sum\limits_{n=1}^{{{N}_{y}}}{B_{jn}^{y}}{{{\ddot{v}}}_{in}} \right)
\end{dmath}


\begin{equation}
\begin{split}
&\left\{ \left[ {{T}_{44}}\left( 1,1 \right)+2{{T}_{44}}\left( 5,1 \right)+{{T}_{44}}\left( 2,1 \right) \right]\left( \sum\limits_{m=1}^{{{N}_{\xi }}}{\bar{D}_{im}^{\xi }}w_{mj}^{b}+B_{i1}^{\xi }\kappa _{1j}^{bx}+B_{i1}^{\xi }\kappa _{{{N}_{\xi }}j}^{b\xi } \right)+ \right.\\ 
&\left[ {{T}_{44}}\left( 1,2 \right) \right.+2{{T}_{44}}\left( 5,2 \right)+\left. {{T}_{44}}\left( 2,2 \right) \right]\left( \sum\limits_{n=1}^{{{N}_{\eta }}}{\bar{D}_{jn}^{\eta }w_{in}^{b}}+B_{j1}^{\eta }\kappa _{i1}^{b\eta }+B_{j1}^{\eta }\kappa _{i{{N}_{\eta }}}^{b\eta } \right)+\\
&\left[ {{T}_{44}}\left( 1,3 \right) \right.+2{{T}_{44}}\left( 5,3 \right)+\left. {{T}_{44}}\left( 2,3 \right) \right]\sum\limits_{n=1}^{{{N}_{\eta }}}{A_{jn}^{\eta }}\left( \sum\limits_{m=1}^{{{N}_{\xi }}}{\bar{C}_{im}^{\xi }}w_{mn}^{b}+A_{i1}^{\xi }\kappa _{1n}^{b\xi } \right.+A_{i{{N}_{\xi }}}^{\xi }.\\ 
&\left. \kappa _{{{N}_{\xi }}n}^{b\xi } \right)+\left[ {{T}_{44}}\left( 1,4 \right)+2{{T}_{44}}\left( 5,4 \right)+{{T}_{44}}\left( 2,4 \right) \right]\sum\limits_{m=1}^{{{N}_{\xi }}}{A_{im}^{\xi }}\left( \sum\limits_{n=1}^{{{N}_{\eta }}}{\bar{C}_{jn}^{\eta }}w_{mn}^{b} \right.+A_{j1}^{\eta }\kappa _{1n}^{b\eta }\\
&\left. +A_{j{{N}_{\eta }}}^{\eta }\kappa _{{{N}_{\eta }}n}^{b\eta } \right)+\left. \left[ {{T}_{44}}\left( 1,5 \right)+2{{T}_{44}}\left( 5,5 \right)+{{T}_{44}}\left( 2,5 \right) \right]\sum\limits_{m=1}^{{{N}_{\xi }}}{\sum\limits_{n=1}^{{{N}_{\eta }}}{B_{im}^{\xi }B_{jn}^{\eta }}w_{mn}^{b}} \right\}2\mu {{\tau }^{s}}\\
&-2\mu {{\tau }^{s}}\left\{ \left[ {{T}_{44}}\left( 1,1 \right)\hspace{0.15 cm}+ \right.2{{T}_{44}}\left( 5,1 \right)\hspace{0.15 cm}+\left. {{T}_{44}}\left( 2,1 \right) \right]\sum\limits_{m=1}^{{{N}_{\xi }}}{D_{im}^{\xi }}w_{mj}^{s}\hspace{0.15 cm}+ \right.\left[ {{T}_{44}}\left( 1,2 \right) \right.+\\
& 2{{T}_{44}}\left( 5,2 \right)+\left. {{T}_{44}}\left( 2,2 \right) \right]\sum\limits_{n=1}^{{{N}_{\eta }}}{D_{jn}^{\eta }w_{in}^{s}}+\left[ {{T}_{44}}\left( 1,3 \right) \right.+2{{T}_{44}}\left( 5,3 \right)+\left. {{T}_{44}}\left( 2,3 \right) \right].\\ 
&\sum\limits_{m=1}^{{{N}_{\xi }}}{\sum\limits_{n=1}^{{{N}_{\eta }}}{C_{im}^{\xi }A_{jn}^{\eta }}w_{mn}^{s}}+\left[ {{T}_{44}}\left( 1,4 \right)+2{{T}_{44}}\left( 5,4 \right)+{{T}_{44}}\left( 2,4 \right) \right]\sum\limits_{m=1}^{{{N}_{\xi }}}{\sum\limits_{n=1}^{{{N}_{\eta }}}{A_{im}^{\xi }C_{jn}^{\eta }}w_{mn}^{s}}+\\ 
&\left. \left[ {{T}_{44}}\left( 1,5 \right)+2{{T}_{44}}\left( 5,5 \right)+{{T}_{44}}\left( 2,5 \right) \right]\sum\limits_{m=1}^{{{N}_{\xi }}}{\sum\limits_{n=1}^{{{N}_{\eta }}}{B_{im}^{\xi }B_{jn}^{\eta }}w_{mn}^{s}} \right\}+\left( kGh+2{{\tau }^{s}} \right).\\
&\left[ {{T}_{22}}\left( 1,1 \right)\sum\limits_{m=1}^{{{N}_{\xi }}}{B_{im}^{\xi }} \right.w_{mj}^{s}+{{T}_{22}}\left( 1,2 \right)\sum\limits_{n=1}^{{{N}_{\eta }}}{B_{jn}^{\eta }}w_{in}^{s}+{{T}_{22}}\left( 1,3 \right)\left. \sum\limits_{m=1}^{{{N}_{\xi }}}{\sum\limits_{n=1}^{{{N}_{\eta }}}{A_{im}^{\xi }A_{jn}^{\eta }w_{mn}^{s}}} \right]\\ 
&+\left( 2{{\tau }^{s}}+\mu {{m}_{0}}\frac{{{\partial }^{2}}}{\partial {{t}^{2}}} \right)\left[ {{T}_{22}}\left( 1,1 \right)\sum\limits_{m=1}^{{{N}_{\xi }}}{B_{im}^{\xi }} \right.\left( w_{mj}^{b}+w_{mj}^{s} \right)+{{T}_{22}}\left( 1,2 \right)\sum\limits_{n=1}^{{{N}_{\eta }}}{B_{jn}^{\eta }}w_{in}^{b}\\
&\left. +w_{in}^{s} \right)+\left. \sum\limits_{m=1}^{{{N}_{\xi }}}{\sum\limits_{n=1}^{{{N}_{\eta }}}{A_{im}^{\xi }A_{jn}^{\eta }\left( w_{mn}^{b}+w_{mn}^{s} \right)}} \right]={{m}_{0}}\frac{{{\partial }^{2}}\left( w_{ij}^{b}+w_{ij}^{s} \right)}{\partial {{t}^{2}}} 
\end{split}
\end{equation}
\end{document}

Answer 1

In my opinion the most important point is that the structure of the equations should be transparent to the reader. Automatic breaking of the equations usually fails dismally on this, despite noble efforts; making all lines the same length is far far worse.

I'll concentrate on your first example.

As a mathematician, I would seriously consider changing the notation: every sum in your example is just some matrix multiplication and I would want to just write the first sum as B u (or possibly (B_i^x) (u)_j) with notation appropriately explained in the surrounding text. Or you could use the Einstein summation convention, where repeated indices are automatically summed over. However, these approaches may be out of court.

With the given notation I would make the following points:

• Don't use automatic sizing with \left and \right, use the specific commands \bigl, \Bigl, \biggl, \Biggl and the right variants aggressively to emphasise the structure of the equation.
• Break lines at logical points in the equation: at major relations =, then +; avoid breaking up logical units.
• Put relation signs at the beginning of the next line, not the end of the current.
• Use indentation to help the visualisation of the structure.

As regards your specific coding

• Don't overuse { } - too many brackets make unreadable code.
• The \limits command is not necessary in display mode.
• Indent the source so that it is readable.

Here is an updated version of your first equation

\documentclass{article}

\usepackage[fleqn]{amsmath}
\usepackage{amssymb}

\begin{document}

\begin{align*}
  &\bigl( \hat{E}h+2E^s \bigr)
  \Biggl[ 
    \sum_{m=1}^{N_x} B_{im}^x u_{mj}
    + \biggl( \sum_{m=1}^{N_x} A_{im}^x w_{mj} \biggr)
      \biggl( \sum_{m=1}^{N_x} B_{im}^x w_{mj} \biggr)
  \Biggr]\\
  &\quad+
    \bigl( \nu \hat{E}h+Gh+2E^s \bigr) \\
    &\qquad \cdot
     \Biggl[ 
       \sum_{m=1}^{N_x} \sum_{n=1}^{N_y} A_{im}^x A_{jn}^y v_{mn}
       + \biggl( \sum_{n=1}^{{N_y}}{A_{jn}^y}{w_{in}} \biggr)
       \biggl(\sum_{m=1}^{N_x} \sum_{n=1}^{N_y} A_{im}^x A_{jn}^y w_{mn} \biggl)
      \Biggr] \\
    &\qquad \cdot
      \bigl[ Gh+2(2\mu^s - \tau^s)\bigr]
      \Biggl[
        \sum_{n=1}^{N_y} B_{jn}^y u_{in}
        + \biggl( \sum_{m=1}^{N_x} A_{im}^x w_{mj} \biggr)
          \biggl( \sum_{n=1}^{N_y} B_{jn}^y w_{in} \biggr) 
      \Biggr] \\
  &\quad = \rho h{\ddot{u}_{ij}}
     - \mu \rho h
       \biggl(
         \sum_{m=1}^{N_x} B_{im}^x \ddot{u}_{mj}
         + \sum_{n=1}^{N_y} B_{jn}^y \ddot{u}_{in}
       \biggr)  
\end{align*}

\end{document}

Reading the documentation associated with amsmath will provide lots of extra advice and further references.