Math & Science ⇒ special layout for huge equations

[gmedina]

...So can I change those values for a single page only?
Would it even be possible to create a minipage which has a smaller left margin and a wider textwidth than the rest of the page?
If the answer to any of those questions is yes, then: how?

The asnwer is, indeed yes. You can use, for example the adjustwidth environment provided by the changepage package to change the page layout for your equation (I don't like very much this option from a typographical standpoint; I would suggest its use if and only if there's no other choice). A little example, with your code:

Code: Select all

\documentclass[a4paper]{report}
\pagestyle{plain}
\usepackage{amsmath}
\usepackage{changepage}
\newcommand{\spsi}{\hspace{1pt}\mathrm{s}\delta\hspace{1pt}}
\newcommand{\cpsi}{\hspace{1pt}\mathrm{c}\delta\hspace{1pt}}
\newcommand{\salpha}[1]{\hspace{1pt}\mathrm{s}\alpha_#1\hspace{1pt}}
\newcommand{\ssalpha}[1]{\hspace{1pt}\mathrm{s}^2\alpha_#1\hspace{1pt}}
\newcommand{\calpha}[1]{\hspace{1pt}\mathrm{c}\alpha_#1\hspace{1pt}}
\newcommand{\csalpha}[1]{\hspace{1pt}\mathrm{c}^2\alpha_#1\hspace{1pt}}

\begin{document}

\begin{adjustwidth}{-3cm}{}
\begin{align}
L=&\frac{1}{2} m_v(\dot{x}^2+\dot{y}^2+\dot{z}^2)+2m_w(\dot{x}^2+\dot{y}^2+\overline{\dot{z}_{ij}^2})\qquad+2m_w\cdot\nonumber\\
&[\nonumber\\
&\quad2\dot{x}\{(\dot{z}-\overline{\dot{z}_{ij}})[\cpsi\gamma+\spsi\epsilon]+\nonumber\\
&\qquad\dot{\delta}[(-\spsi\gamma+\cpsi\epsilon)(z-\overline{z_{ij}})-\spsi(1+\frac{1}{2}\gamma^2)\overline{l_j}]+\nonumber\\
&\qquad\dot{\epsilon}[(\cpsi\epsilon\gamma+\spsi(1+\epsilon^2))(z-\overline{z_{ij}})]+\nonumber\\
&\qquad\dot{\gamma}\cpsi[(1+\frac{1}{2}\epsilon^2+\gamma^2)(z-\overline{z_{ij}})+\gamma \overline{l_j}]\}\nonumber\\
%
&+2\dot{y}\{(\dot{z}-\overline{\dot{z}_{ij}})[\spsi\gamma-\cpsi\epsilon]+\nonumber\\
&\qquad\dot{\delta}[(\cpsi\gamma+\spsi\epsilon)(z-\overline{z_{ij}})+\cpsi(1+\frac{1}{2}\gamma^2)\overline{l_j}]+\nonumber\\
&\qquad\dot{\epsilon}[(\spsi\epsilon\gamma-\cpsi(1+\epsilon^2))(z-\overline{z_{ij}})]+\nonumber\\
&\qquad\dot{\gamma}\spsi[(1+\frac{1}{2}\epsilon^2+\gamma^2)(z-\overline{z_{ij}})+\gamma \overline{l_j}]\}\nonumber\\
%
&+(\dot{z}^2-2\dot{z}\overline{\dot{z}_{ij}}+\overline{\dot{z}_{ij}^2})[\gamma^2+\epsilon^2]\nonumber\\
%
&+\dot{\delta}^2[(\gamma^2+\epsilon^2)(z^2-2z\overline{z_{ij}}+\overline{z_{ij}^2})+(1+\gamma^2)\overline{l_j^2}+(1+\epsilon^2)w^2+\nonumber\\
&\qquad2\gamma(z\overline{l_j}-\overline{z_{ij}l_j})+2\epsilon\overline{z_{ij}w_i}]\nonumber\\
%
&+\dot{\epsilon}^2[(1+2\epsilon^2)(z^2-2z\overline{z_{ij}}+\overline{z_{ij}^2})+(\epsilon^2+\gamma^2)w^2+2\epsilon\overline{z_{ij}w_i}]\nonumber\\
%
&+\dot{\gamma}^2[(1+\epsilon^2+2\gamma^2)(z^2-2z\overline{z_{ij}}+\overline{z_{ij}^2})+\gamma^2\overline{l_j^2}+\epsilon^2w^2+\nonumber\\
&\qquad 2\gamma(z\overline{l_j}-\overline{z_{ij}l_j})+2\epsilon\overline{z_{ij}w_i}] \nonumber\\
%
&+2\dot{\delta}[-\epsilon(\dot{z}\overline{l_j}-\overline{\dot{z}_{ij}l_ij})+\gamma\overline{\dot{z}_{ij}w_i}]
+2\dot{\epsilon}[\epsilon(\dot{z} z-\dot{z}\overline{z_{ij}}-\overline{\dot{z}_{ij}}z+\overline{\dot{z}_{ij}z_{ij}})+(\gamma^2+\epsilon^2)\overline{\dot{z}_{ij}w_i}] \nonumber\\
&+2\dot{\gamma}\gamma[(\dot{z} z-\dot{z}\overline{z_{ij}}-\overline{\dot{z}_{ij}}z+\overline{\dot{z}_{ij}z_{ij}}) +\gamma(\dot{z}\overline{l_j}-\overline{\dot{z}_{ij}l_j})+\epsilon\overline{\dot{z}_{ij} w_i}]\nonumber\\
%
&+2\dot{\delta}\dot{\epsilon}[-\gamma(z^2-2z\overline{z_{ij}}+\overline{z_{ij}^2})+
\gamma w^2-(1+\epsilon^2+\frac{1}{2}\gamma^2)(z\overline{l_j}-\overline{z_{ij}l_j})]\nonumber\\
%
&+2\dot{\delta}\dot{\gamma}[\epsilon(z^2-2z\overline{z_{ij}}+\overline{z_{ij}^2})+
\epsilon w^2+\epsilon\gamma(z\overline{l_j}-\overline{z_{ij}l_j})+(1+2\epsilon^2+\gamma^2)\overline{z_{ij}w_i}]\nonumber\\
%
&+2\dot{\epsilon}\dot{\gamma}\gamma[\epsilon(z^2-2z\overline{z_{ij}}+\overline{z_{ij}^2})+\epsilon w^2+\overline{z_{ij}w_i}]\nonumber\\
&]\nonumber\\
%
&+\frac{1}{2}(I_{vx}+I_{wr}(2+\csalpha{l}+\csalpha{r})+I_{wy}(\ssalpha{l}+\ssalpha{r}))
[\dot{\delta}^2\gamma^2+\dot{\epsilon}^2(1-\gamma^2)-2\dot{\delta}\dot{\epsilon}\gamma]\nonumber\\
&+\frac{1}{2}(I_{vy}+I_{wy}(2+\csalpha{l}+\csalpha{r})+I_{wr}(\ssalpha{l}+\ssalpha{r}))[\dot{\delta}^2\epsilon^2+\dot{\gamma}^2+2\dot{\delta}\dot{\gamma}\epsilon]\nonumber\\
&+\frac{1}{2}(I_{vz}+4I_{wr})[\dot{\delta}^2(1-\epsilon^2-\gamma^2)+\dot{\epsilon}^2\gamma^2+2\dot{\delta}\dot{\epsilon}\gamma]\nonumber\\
%
&+I_{vxz}[\dot{\delta}^2\gamma-\dot{\epsilon}^2\gamma-\dot{\delta}\dot{\epsilon}(1-\frac{1}{2}\epsilon^2-2\gamma^2)]
%
+\frac{1}{2} I_{wy}(\dot{\zeta}_{lf}^2+\dot{\zeta}_{rf}^2+\dot{\zeta}_{lb}^2+\dot{\zeta}_{rb}^2)\nonumber\\
%
&-I_{wy}[(\dot{\delta}\epsilon+\dot{\gamma})(\dot{\zeta}_{lf}\calpha{l}+\dot{\zeta}_{rf}\calpha{r}+\dot{\zeta}_{lb}+\dot{\zeta}_{rb})
+(\dot{\delta}\gamma-\dot{\epsilon}(1-\frac{1}{2}\gamma^2))(\dot{\zeta}_{lf}\salpha{l}+\dot{\zeta}_{rf}\salpha{r})]\nonumber\\
%
&+(I_{wy}-I_{wr})(\salpha{l}\calpha{l}+\salpha{r}\calpha{r}) [\dot{\delta}^2\epsilon\gamma-\dot{\epsilon}\dot{\gamma}(1-\frac{1}{2}\gamma^2)-\dot{\delta}\dot{\epsilon}\epsilon+\dot{\delta}\dot{\gamma}\gamma]\nonumber\\
%
&+I_{wr}[\frac{1}{2}(\dot{\alpha}_l^2+\dot{\alpha}_r^2)+(\dot{\delta}(1-\frac{1}{2}\epsilon^2-\frac{1}{2}\gamma^2)+\dot{\epsilon}\gamma)(\dot{\alpha}_l+\dot{\alpha}_r)]\nonumber\\
%
&-m_v\,g\,z-4m_w\,g\,\overline{z_{ij}}
\end{align}
\end{adjustwidth}
\end{document}

[Juanjo]

In my opinion the problem is not really the large size of the equations, but that they are not sufficiently organized and well written. The following code shows how you can split every long relation in two or more lines. There is even room for the equation number:

Code: Select all

\documentclass[a4paper]{report}
\pagestyle{plain}
\usepackage{amsmath}

\newcommand{\spsi}{\mathrm{s}\delta}
\newcommand{\cpsi}{\mathrm{c}\delta}
\newcommand{\salpha}[1]{\mathrm{s}\alpha_#1}
\newcommand{\ssalpha}[1]{\mathrm{s}^2\alpha_#1}
\newcommand{\calpha}[1]{\mathrm{c}\alpha_#1}
\newcommand{\csalpha}[1]{\mathrm{c}^2\alpha_#1}

\begin{document}

\noindent Text text text \hfill text text text \hfill text text text.

\allowdisplaybreaks

\newcommand{\tab}{\hspace{1em}}
\begin{equation}
\begin{split}
 L={}&\frac{1}{2} m_v(\dot{x}^2+\dot{y}^2+\dot{z}^2)+2m_w(\dot{x}^2+\dot{y}^2+\overline{\dot{z}_{ij}^2}) \\
  &\tab+2m_w
  \begin{aligned}[t]
    \biggl[
%
    &2\dot{x}
    \begin{aligned}[t]
      \Bigl\{ &(\dot{z}-\overline{\dot{z}_{ij}})[\cpsi\gamma+\spsi\epsilon] \\
      &\tab+\dot{\delta}\bigl[(-\spsi\gamma+\cpsi\epsilon)(z-\overline{z_{ij}})
       -\spsi(1+\gamma^2/2)\overline{l_j}\bigr] \\
      &\tab+\dot{\epsilon}\bigl[(\cpsi\epsilon\gamma+\spsi(1+\epsilon^2))(z-\overline{z_{ij}})\bigr] \\
      &\tab+\dot{\gamma}\cpsi\bigl[(1+\epsilon^2/2+\gamma^2)(z-\overline{z_{ij}})
       +\gamma \overline{l_j}\bigr]
      \Bigr\}
    \end{aligned} \\
%
    &\tab+2\dot{y}
    \begin{aligned}[t]
      \Bigl\{ &(\dot{z}-\overline{\dot{z}_{ij}})[\spsi\gamma-\cpsi\epsilon] \\
      &\tab+\dot{\delta}\bigl[(\cpsi\gamma+\spsi\epsilon)(z-\overline{z_{ij}})
       +\cpsi(1+\gamma^2/2)\overline{l_j}\bigr] \\
      &\tab+\dot{\epsilon}\bigl[(\spsi\epsilon\gamma-\cpsi(1+\epsilon^2))(z-\overline{z_{ij}})\bigr] \\
      &\tab+\dot{\gamma}\,\spsi\bigl[(1+\epsilon^2/2+\gamma^2)(z-\overline{z_{ij}})
       +\gamma \overline{l_j}\bigr]
      \Bigr\}
    \end{aligned} \\
%
    &\tab+2\dot{\delta}\dot{\gamma}
    \begin{aligned}[t]
      \Bigl[ &\epsilon\bigl(z^2-2z\overline{z_{ij}}+\overline{z_{ij}^2}\bigr)
        +\epsilon w^2 \\
      &\tab+\epsilon\gamma(z\overline{l_j}-\overline{z_{ij}l_j})
        +(1+2\epsilon^2+\gamma^2)\overline{z_{ij}w_i}
     \Bigr]
    \end{aligned} \\
%
    &\tab+2\dot{\epsilon}\dot{\gamma}\gamma\Bigl[\epsilon\bigl(z^2-2z\overline{z_{ij}}
    +\overline{z_{ij}^2}\bigr)+\epsilon w^2+\overline{z_{ij}w_i}\Bigr] 
%
    \biggr]
  \end{aligned} \\
%
  &\tab+
  \begin{aligned}[t]
    &\frac{1}{2} \bigl(I_{vx}+I_{wr}(2+\csalpha{l}+\csalpha{r})+I_{wy}(\ssalpha{l}+\ssalpha{r})\bigr) \\
    &\tab\times \bigl[\dot{\delta}^2\gamma^2+\dot{\epsilon}^2(1-\gamma^2)
       -2\dot{\delta}\dot{\epsilon}\gamma\bigr] 
  \end{aligned}\\
  &\tab+
  \begin{aligned}[t]
    &\frac{1}{2} \bigl(I_{vy}+I_{wy}(2+\csalpha{l}+\csalpha{r})+I_{wr}(\ssalpha{l}
     +\ssalpha{r}) \bigr) \\
    &\tab\times\bigl[\dot{\delta}^2\epsilon^2+\dot{\gamma}^2+2\dot{\delta}\dot{\gamma}\epsilon \bigr]
  \end{aligned} \\
  &\tab+\frac{1}{2}(I_{vz}+4I_{wr}) \bigl[\dot{\delta}^2(1-\epsilon^2-\gamma^2)+\dot{\epsilon}^2\gamma^2
   +2\dot{\delta}\dot{\epsilon}\gamma \bigr]\\
%
  &\tab+I_{vxz} \bigl[\dot{\delta}^2\gamma-\dot{\epsilon}^2\gamma-\dot{\delta}\dot{\epsilon}
   (1-\epsilon^2/2-2\gamma^2) \bigr] \\
%
  &\tab+\frac{1}{2} I_{wy} \bigl(\dot{\zeta}_{lf}^2+\dot{\zeta}_{rf}^2+\dot{\zeta}_{lb}^2
   +\dot{\zeta}_{rb}^2 \bigl)\\
%
  &\tab-I_{wy}
  \begin{aligned}[t]
    \Bigl[ &\bigl(\dot{\delta}\epsilon+\dot{\gamma} \bigr)
    \bigl(\dot{\zeta}_{lf}\calpha{l}+\dot{\zeta}_{rf}\calpha{r}
    +\dot{\zeta}_{lb}+\dot{\zeta}_{rb} \bigr) \\
    &\tab+\bigl(\dot{\delta}\gamma-\dot{\epsilon}(1-\gamma^2/2) \bigr) \bigl(\dot{\zeta}_{lf}\salpha{l}
    +\dot{\zeta}_{rf}\salpha{r}\bigr)\Bigr]
  \end{aligned} \\
%
  &\tab+(I_{wy}-I_{wr})(\salpha{l}\calpha{l}+\salpha{r}\calpha{r}) \bigl[\dot{\delta}^2\epsilon\gamma
  -\dot{\epsilon}\dot{\gamma}(1-\gamma^2/2)-\dot{\delta}\dot{\epsilon}\epsilon
  +\dot{\delta}\dot{\gamma}\gamma \bigr]\\
%
  &\tab+I_{wr}\Bigl[\tfrac{1}{2}(\dot{\alpha}_l^2+\dot{\alpha}_r^2)+ \bigl(\dot{\delta}
  (1-\epsilon^2/2-\gamma^2/2)+\dot{\epsilon}\gamma \bigr)(\dot{\alpha}_l+\dot{\alpha}_r)\Bigr]\\
%
  &\tab-m_v\,g\,z-4m_w\,g\,\overline{z_{ij}}
\end{split}
\end{equation}

\end{document}

The above code reproduces most of the sample equation you provided. You should complete it. Please note the following questions:

• Use the aligned environment, for example, to divide long expressions. In each secondary level, indent the second and subsequent lines. I've done that with an own defined macro called \tab that you can adjust to fit your needs.
• The size of delimiters is important to help reading expressions.
• If possible, avoid fractions like \frac{1}{2} inside complex expressions. For example, instead of, say, \frac{1}{2}\epsilon, you can simply write \epsilon/2, or, at least, \tfrac{1}{2}\epsilon.
• Binary operators should be at the beginning of lines, not at the end.
• Don't include spaces in the macro definition. Add them when really needed with macros like \, , \; , \: etc.
• Don't use \nonumber to suppress numbering inside an amsmath environment. Use \notag instead.
• The combination of equation and split environments provides a unique centered equation number. If you want such a number at the bottom line, use the tbtags option when loading amsmath. Instead, you can also replace equation + split by a single align environment, adding \notag in each not numbered line.
• The \allowdisplaybreaks command instructs LaTeX to allow page breaks inside displayed equations. Useful if a very long equation needs to expand through more than one page.

[tyltus]

Sorry for the late answer, I was occupied with some more calculations rather than the report the past few months...

The asnwer is, indeed yes. You can use, for example the adjustwidth environment provided by the changepage package to change the page layout for your equation (I don't like very much this option from a typographical standpoint; I would suggest its use if and only if there's no other choice).

Thank you very much, this is indeed exactly what I was looking for! I totally agree that this is something that you should avoid whenever possible but its good to know that there is a possibility.

In my opinion the problem is not really the large size of the equations, but that they are not sufficiently organized and well written. Please note the following questions:

• Use the aligned environment, for example, to divide long expressions. In each secondary level, indent the second and subsequent lines. I've done that with an own defined macro called \tab that you can adjust to fit your needs.
• The size of delimiters is important to help reading expressions.
• If possible, avoid fractions like \frac{1}{2} inside complex expressions. For example, instead of, say, \frac{1}{2}\epsilon, you can simply write \epsilon/2, or, at least, \tfrac{1}{2}\epsilon.
• Binary operators should be at the beginning of lines, not at the end.
• Don't include spaces in the macro definition. Add them when really needed with macros like \, , \; , \: etc.
• Don't use \nonumber to suppress numbering inside an amsmath environment. Use \notag instead.
• The combination of equation and split environments provides a unique centered equation number. If you want such a number at the bottom line, use the tbtags option when loading amsmath. Instead, you can also replace equation + split by a single align environment, adding \notag in each not numbered line.
• The \allowdisplaybreaks command instructs LaTeX to allow page breaks inside displayed equations. Useful if a very long equation needs to expand through more than one page.

This list also proved to be very helpful! Indeed, by now I decided not to include the above mentioned equation in the report, but this still helped me keeping a better structure and I will gladly use it in my upcomming reports.

A big thank you again to everyone who tried to help!
Best regards
Martin