[Tex/LaTex] Compact collapsing of equations and paragraphs


I want to duplicate the compact look of G. K. Batchelor's fluid dynamics book. Where a paragraph terminates such that the mathematical expression can collapse up into the vertical space of the paragraph, the expression moves up. If that makes no sense, see it on Google Books.

Can the align environment do this automatically? Or do I need to use another environment? I'm not aware of any way to do this automatically.

Best Answer

Here is a LaTeX approach at duplicating the typesetting in your link, as well as using @morbusg's \abovedisplayshortskip of -.5\baselineskip (plus some glue):

enter image description here

\usepackage[margin=2.05in]{geometry}% http://ctan.org/pkg/geometry
\usepackage{amsmath}% http://ctan.org/pkg/amsmath
\newcommand{\pfrac}[2]{\frac{\partial #1}{\partial #2}}% Partial derivative
\setlength{\abovedisplayshortskip}{-.5\baselineskip plus 3pt}% Original value: 0pt plus 3pt
\noindent \textit{Local variation of the velocity magnitude}

Some simple but useful results follow immediately from the expression 
for local vorticity in terms of rectuangular co-ordinates with axes parallel 
to the location directions of~$\mathbf{u}$, of the principal normal to the streamline 
(directed towards the centre of curvature), and of the binomial to the 
streamline. If $(s,n,b)$ represent co-ordinates in these three dimensions 
respectively, and $(u,v,w)$ are the corresponding velocity components, we 
  v=w=0, \quad 
  u=q, \quad 
  \pfrac{v}{s}=\frac{q}{R}, \quad 
locally, where~$R$ is the local radius of curvature of the streamline. The 
components of the vorticity locally are then
  \omega_s=\pfrac{w}{n}-\pfrac{v}{b}, \quad 
  \omega_n=\pfrac{u}{b}, \quad 
locally. Hence, in irrotational flow we have
  \pfrac{q}{n}=\frac{q}{R}, \quad \pfrac{q}{b}=0. \tag{6.2.13}\label{irrotational_flow}

The first of the relations~\eqref{irrotational_flow} shows that, when the streamlines \ldots


geometry was used to reduce the margins and mimic the linked output.

The only difference in the output was from typesetting the line that has a centered alignment with respect to the text block, while still having text left-aligned ("Moreover," in this case). Some "trickery" (via \rlap) was used to obtain this, but that could also have been what the author did in their markup. As @egreg mentioned in comment, the use of \leavevmode is necessary if the paragraph was preceded by a blank line. As such, and for completeness (since it does no harm here...), I've added \leavevmode.

From a pedagogical point of view, the use of \abovedisplayshortskip is taken from the width of the (single) last line in the preceding paragraph. As such, it would take more than just modifying \abovedisplayshortskip to accommodate the display presented in your link for a general use-case when the previous paragraph consists of a single line, unless you're willing to do some compacting yourself using manual intervention (as I did in my example).

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