Split equations inside the align environment

Question

I have some equations that I have written inside the align environment. Because some of these equations are rather long, they tend to spill over the page. I have tried using the split environment inside the align environment to split some of these equations over two lines but this appears to break the code. I would be very grateful for some advice on how to modify my code in order to achieve the desired outcome. My (original) code and the output produced by LaTeX are shown below.

\documentclass[11pt]{book}
\usepackage{amsmath,amsfonts,amssymb,amsthm, bm}

\begin{document}

\begin{align}
\dot{v}       & = \dfrac{1}{m}[T\cos\beta\cos(\alpha+\epsilon)-D]-g\sin\gamma +\dot{w}_{x} \cos\gamma\cos\chi+\dot{w}_{y}\cos\gamma\sin\chi \\[2pt]
\dot{\gamma}  & = \dfrac{1}{m}[(Y-T\sin\beta\cos(\alpha+\epsilon))\sin\mu + (T\sin(\alpha +\epsilon)+L)\cos\mu] - \dfrac{g}{v}\cos\gamma +\dfrac{1}{v}[\dot{w}_{x}\sin\gamma\cos\chi + \dot{w}_{y}\sin\gamma\sin\chi] \\[2pt]
\dot{\chi}    & = \dfrac{1}{mv\cos\gamma}[(L+T\sin(\alpha+\epsilon) )\sin\mu + (T\sin\beta \cos(\alpha  + \epsilon) - Y)\cos\mu] + \dfrac{1}{v\cos\gamma}[\dot{w}_{x}\sin\chi-\dot{w}_{y}\cos\chi] 
\end{align}

\end{document} 

Answer 1

You can use split inside align:

\documentclass[11pt]{book}
\usepackage{amsmath,amsfonts,amssymb,amsthm, bm}

\begin{document}

\begin{align}
\begin{split}
  \dot{v}     & = \dfrac{1}{m}[T\cos\beta\cos(\alpha+\epsilon)-D]-g\sin\gamma \\
              &\qquad +\dot{w}_{x} \cos\gamma\cos\chi+\dot{w}_{y}\cos\gamma\sin\chi
\end{split}
\\[2ex]
\begin{split}
\dot{\gamma}  & = \dfrac{1}{m}[(Y-T\sin\beta\cos(\alpha+\epsilon))\sin\mu \\
              &\qquad + (T\sin(\alpha +\epsilon)+L)\cos\mu] - \dfrac{g}{v}\cos\gamma \\
              &\qquad +\dfrac{1}{v}[\dot{w}_{x}\sin\gamma\cos\chi + \dot{w}_{y}\sin\gamma\sin\chi]
\end{split}
\\[2ex]
\begin{split}
\dot{\chi}    & = \dfrac{1}{mv\cos\gamma}[(L+T\sin(\alpha+\epsilon) )\sin\mu \\
              &\qquad + (T\sin\beta \cos(\alpha  + \epsilon) - Y)\cos\mu] \\
              &\qquad + \dfrac{1}{v\cos\gamma}[\dot{w}_{x}\sin\chi-\dot{w}_{y}\cos\chi]
\end{split}
\end{align}

\end{document} 

Answer 2

Choose manually some suitable points at which the equations can break and add the \notag or \nonumber command to remove the equation label at that line.

\documentclass[11pt]{book}
\usepackage{amsmath,amsfonts,amssymb,amsthm, bm}

\begin{document}

\begin{align}
\dot{v}        ={} &\dfrac{1}{m}[T\cos\beta\cos(\alpha+\epsilon)-D]-g\sin\gamma +\dot{w}_{x} \cos\gamma\cos\chi+\dot{w}_{y}\cos\gamma\sin\chi \\[2pt]
\dot{\gamma}   ={} &\dfrac{1}{m}[(Y-T\sin\beta\cos(\alpha+\epsilon))\sin\mu + (T\sin(\alpha +\epsilon)+L)\cos\mu] - \dfrac{g}{v}\cos\gamma \notag\\
                   &{}+\dfrac{1}{v}[\dot{w}_{x}\sin\gamma\cos\chi+ \dot{w}_{y}\sin\gamma\sin\chi] \\[2pt]
\dot{\chi}     ={} &\dfrac{1}{mv\cos\gamma}[(L+T\sin(\alpha+\epsilon) )\sin\mu + (T\sin\beta \cos(\alpha  + \epsilon) - Y)\cos\mu] \notag\\ 
                   &{}+\dfrac{1}{v\cos\gamma}[\dot{w}_{x}\sin\chi-\dot{w}_{y}\cos\chi] 
\end{align}

\end{document}

Answer 3

Here is a solution with aligned and the fleqn environment from nccmath:

\documentclass[11pt]{book}
\usepackage{mathtools,amsfonts,amssymb,amsthm, bm, nccmath}
%\usepackage{geometry}
\usepackage{showframe}
\renewcommand\ShowFrameLinethickness{0.3pt}

\begin{document}

\begin{fleqn}% comment if you uncomment \usepackage{geometry}
  \begin{align}
    \dot{v} & = \dfrac{1}{m}[T\cosβ\cos(\alpha+ϵ)-D]-g\sinγ+\dot{w}_{x} \cosγ\cos\chi+\dot{w}_{y}\cosγ\sinχ\!\! \\[2pt]
    \dot{γ} & =\begin{aligned}[t] \dfrac{1}{m}\bigl[(Y-T\sinβ\cos(\alpha+ϵ))\sinμ+ (T\sin(α+ϵ)+L)\cosμ\bigr] \\[-1.2ex]%
    {}- \dfrac{g}{v}\cosγ+\dfrac{1}{v}\bigl[\dot{w}_{x}\sinγ\cosχ+ \dot{w}_{y}\sinγ\sinχ\bigr]\end{aligned} \\[2pt]
    \dot{χ} & =\begin{aligned}[t] \dfrac{1}{mv\cosγ}\bigl[(L+T\sin(\alpha+ϵ) )\sinμ+ (T\sinβ\cos(α+ ϵ) - Y)\cosμ\bigr] \\[-1.2ex]%
    {}+ \dfrac{1}{v\cosγ}\bigl[\dot{w}_{x}\sin\chi-\dot{w}_{y}\cosχ\bigr]\end{aligned}
  \end{align}
\end{fleqn}

\end{document} 

Note that, if you load geometry, you have more sensible outside margins, so you don't need any more fleqn:

Answer 4

You can keep using the align environment. At suitable locations, insert \notag \\ &\qquad directives to (a) introduce line breaks and (b) provide an alignment anchor for the remaining stub.

\documentclass[11pt]{book}
\usepackage{amsmath}

\begin{document}
\begin{align}
\dot{v}       
&= \frac{1}{m}\bigl[T\cos\beta\cos(\alpha+\epsilon)-D\bigr]-g\sin\gamma \notag\\
&\qquad +\dot{w}_x \cos\gamma\cos\chi+\dot{w}_y\cos\gamma\sin\chi \\[2pt]
\dot{\gamma} 
&= \frac{1}{m}\bigl[(Y-T\sin\beta\cos(\alpha+\epsilon))\sin\mu + (T\sin(\alpha +\epsilon)+L)\cos\mu\bigr]\notag\\
&\qquad -\frac{g}{v}\cos\gamma +\frac{1}{v}(\dot{w}_x\sin\gamma\cos\chi + \dot{w}_y\sin\gamma\sin\chi) \\[2pt]
\dot{\chi}    
&= \frac{1}{mv\cos\gamma}\bigl[(L+T\sin(\alpha+\epsilon) )\sin\mu + (T\sin\beta \cos(\alpha  + \epsilon) - Y)\cos\mu\bigr] \notag\\
&\qquad +\frac{1}{v\cos\gamma}(\dot{w}_x\sin\chi-\dot{w}_y\cos\chi)
\end{align}

\end{document}