用括号和换行符标记方程式

Question 1

您的代码中有几个错误；的定义\vol不应该有\makebox[0pt]，因为这会使符号的宽度为零。

也\phantom应该是，所以只需使用垂直尺寸。这里\vphantom不需要\left和。\right

我\vol为 STIX Two 字体做了改进，字距更小，上标和下标可调整大小。修改后的定义\diff还允许您将其用于衍生产品。

\documentclass[10pt,twoside,letterpaper,titlepage]{article}

\usepackage{amsmath}
\usepackage{stix2}
\usepackage{varwidth}

\newcommand{\vol}{%
  \mathord{\text{%
    \ooalign{\hfil$V$\hfil\cr\kern0.03em--\hfil\cr}%
  }}%
}
\newcommand{\diff}{\mathop{}\!\mathrm{d}}
%\newcommand{\dd}{\mathrm{d}} % not needed, just use \diff
\newcommand{\btext}[1]{\text{\begin{varwidth}[t]{\textwidth}\centering#1\end{varwidth}}}

\begin{document}

\begin{equation*}
\overbrace{
  \underbrace{\oiiint\limits_{\vol} \rho \vec{f}_b\diff \vol}
    _{\btext{Body forces  \\ (acceleration, emf, \\ gravity, etc.)}}
 -\underbrace{\oiint\limits_SP\diff S}_{\btext{Pressure \\ forces}}
 +\underbrace{\vphantom{\intup\limits_S}\vec{F}_\mu\vphantom{\int\limits_S}}
    _{\btext{Viscous \\ forces}}}^{\vec{F}}
 =\overbrace{\underbrace{\oiint\limits_S (\rho\vec{v}\cdot\diff S)\vec{v}}
    _{m\frac{\diff v}{\diff t}}
 +\underbrace{\frac{\partial}{\partial t}\oiiint\limits_{\vol}\rho \vec{v}\diff \vol}
    _{\vec{v}\frac{\diff m}{\diff t}}}^{\frac{\diff}{\diff t}(m\vec{v})}
\end{equation*}

\end{document}

对于长下标，我利用了varwidth使框尽可能宽的方法。该名称\btext代表“断线（跨行）文本”。

改进的版本，纠正了一些错误的间距：

\documentclass[10pt,twoside,letterpaper,titlepage]{article}

\usepackage{amsmath}
\usepackage{stix2}
\usepackage{varwidth}

\newcommand{\vol}{%
  \mathord{\text{%
    \ooalign{\hfil$V$\hfil\cr\kern0.03em--\hfil\cr}%
  }}%
}
\newcommand{\diff}{\mathop{}\!\mathrm{d}}
%\newcommand{\dd}{\mathrm{d}} % not needed, just use \diff
\newcommand{\btext}[1]{\text{\begin{varwidth}[t]{\textwidth}\centering#1\end{varwidth}}}

\newcommand{\ob}[2]{{\overbrace{#1}^{#2}}}
\newcommand{\ub}[2]{{\underbrace{#1}_{#2}}}


\begin{document}

\begin{equation*}
\ob{
  \ub{\oiiint\limits_{\vol} \rho \vec{f}_b\diff \vol}
     {\btext{Body forces  \\ (acceleration, \\ emf, gravity, etc.)}}
 -\ub{\oiint\limits_SP\diff S}{\btext{Pressure \\ forces}}
 +\ub{\vphantom{\intup\limits_S}\vec{F}_\mu\vphantom{\int\limits_S}}
     {\hspace{-2em}\btext{Viscous \\ forces}\hspace{-2em}}
   }{\vec{F}}
=
\ob{
   \ub{\oiint\limits_S (\rho\vec{v}\cdot\diff S)\vec{v}}{m\frac{\diff v}{\diff t}}
  +\ub{\frac{\partial}{\partial t}\oiiint\limits_{\vol}\rho \vec{v}\diff \vol}
       {\vec{v}\frac{\diff m}{\diff t}}
   }{\frac{\diff}{\diff t}(m\vec{v})}
\end{equation*}

\end{document}

最好使用定义的宏\ob，以便隐藏归因于其标准定义\ub的性质。\mathop\overbrace\underbrace

我会考虑避免过多的括号不足和过度使用。这里我还添加了一些\,上面代码中缺少但确实应该应用的部分。

\documentclass[10pt,twoside,letterpaper,titlepage]{article}

\usepackage{amsmath}
\usepackage{stix2}
\usepackage{varwidth}

\newcommand{\vol}{%
  \mathord{\text{%
    \ooalign{\hfil$V$\hfil\cr\kern0.03em--\hfil\cr}%
  }}%
}
\newcommand{\diff}{\mathop{}\!\mathrm{d}}
%\newcommand{\dd}{\mathrm{d}} % not needed, just use \diff
\newcommand{\btext}[1]{\text{\begin{varwidth}[t]{\textwidth}\centering#1\end{varwidth}}}

\newcommand{\ob}[2]{{\overbrace{#1}^{#2}}}
\newcommand{\ub}[2]{{\underbrace{#1}_{#2}}}


\begin{document}

The force $\vec{F}$ can be split as the sum of
\begin{align*}
&\oiiint\limits_{\vol} \rho \vec{f}_b\diff \vol && \text{Body forces (acceleration, emf, gravity, etc.)} \\
&\oiint\limits_SP\diff S && \text{Pressure forces} \\
&\vec{F}_\mu && \text{Viscous forces}
\end{align*}
and $\frac{\diff}{\diff t}(m\vec{v})=m\frac{\diff\vec{v}}{\diff t}+\vec{v}\,\frac{\diff m}{\diff t}$, where
\begin{align*}
m\frac{\diff\vec{v}}{\diff t}  &= \oiint\limits_S (\rho\vec{v}\cdot\diff S)\vec{v} \\
\vec{v}\,\frac{\diff m}{\diff t} &= \frac{\partial}{\partial t}\oiiint\limits_{\vol}\rho \vec{v}\diff \vol
\end{align*}
so we arrive at the main formula
\begin{equation*}
\oiiint\limits_{\vol} \rho \vec{f}_b\diff \vol +
\oiint\limits_SP\diff S +
\vec{F}_\mu
=
\oiint\limits_S (\rho\vec{v}\cdot\diff S)\vec{v} +
\frac{\partial}{\partial t}\oiiint\limits_{\vol}\rho \vec{v}\diff \vol
\end{equation*}

\end{document}

Answer