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update magnetic flux
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pglpm committed Oct 31, 2024
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12 changes: 8 additions & 4 deletions seven-wonders.tex
Original file line number Diff line number Diff line change
Expand Up @@ -2,7 +2,7 @@
\pdfinclusioncopyfonts=1
%% Author: PGL Porta Mana
%% Created: 2015-05-01T20:53:34+0200
%% Last-Updated: 2024-10-31T11:50:37+0100
%% Last-Updated: 2024-10-31T12:19:57+0100
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\newif\ifanon
\anonfalse
Expand Down Expand Up @@ -5483,9 +5483,13 @@ \section{Formulation and generalities}

\begin{equation}
\label{eq:cons_matter}
\underbracket[0pt]{\yN(\ytf) =\yN(\yti) + \int_{\yti}^{\ytf}\!\!\yJ(t)\,\di t \int_{\yti}^{\ytf}\!\!\ya(t)\,\di t}_{\mathclap{\text{\color{grey}integral form}}}
\underbracket[0pt]{\yN(\ytf) =
\yN(\yti) +
\int_{\yti}^{\ytf}\!\!\yJ(t)\,\di t +
\int_{\yti}^{\ytf}\!\!\ya(t)\,\di t}_{\mathclap{\text{\color{grey}integral form}}}
\qquad\quad
\underbracket[0pt]{\frac{\di\yN(t)}{\di t} = \yJ(t) \ya(t)}_{\mathclap{\text{\color{grey}differential form}}}
\underbracket[0pt]{\frac{\di\yN(t)}{\di t} = \yJ(t) +
\ya(t)}_{\mathclap{\text{\color{grey}differential form}}}
\end{equation}
The supply $\ya$ is usually called \textbf{activity}, and $\ya(t)\equiv 0$ in case of conservation.
\end{definition}
Expand Down Expand Up @@ -6436,7 +6440,7 @@ \subsection{Statics again: cable cars}
\begin{definition}{{Momentum flux allowed in cables and ropes}}
A cable, rope, or similar object can (approximately) only transmit \autoref{sec:tension}{\emph{tensile} momentum flux}, aligned along its axis.
\end{definition}
Pictorially this means that only the momentum flux represented in the left picture below (tension) is physically possible:
Pictorially this means that only the momentum flux represented in the left picture below -- tension -- is physically possible:
\begin{center}
\includegraphics[align=c,width=0.33\linewidth]{images/cabletension.jpg}%
\hfill
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