From 5cc7f50bad779e4f4efb747a74bbce53a7e05cd3 Mon Sep 17 00:00:00 2001
From: "Y. Wang" <yw05@forksworld.de>
Date: Tue, 19 Jul 2022 17:43:30 +0200
Subject: Split manual into multiple files

---
 assets/manual/physics.tex | 47 +++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 47 insertions(+)
 create mode 100644 assets/manual/physics.tex

(limited to 'assets/manual/physics.tex')

diff --git a/assets/manual/physics.tex b/assets/manual/physics.tex
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+\appendix
+\part*{Appendices}
+\addcontentsline{toc}{part}{Appendices}
+
+\section{Physics}\label{s:physics}
+This section is mainly intended as a reference that is provided for convenience.
+
+\subsection{Movement}
+
+\begin{align*}
+  v &= \int a\, dt \\
+  x &= \int v\, dt \\
+\end{align*}
+
+\subsubsection{Constant acceleration}
+\begin{align*}
+  v &= v_0 + at \\
+  x &= x_0 + v_0t + \frac{1}{2}at^2
+\end{align*}
+
+In certain cases, the starting velocity $v_0$ and the target velocity $v_1$ are known:
+\begin{align*}
+  t &= \frac{v_1 - v_0}{a} \\
+  s &= \frac{v_1^2 - v_0^2}{2a}
+\end{align*}
+
+\subsubsection{Acceleration of a train}
+The acceleration of a train is calculate as follows:
+\[a = a_{\text{all}} + a_{\text{locomotive}}\cdot\frac{n_{\text{locomotives}}}{n_{\text{wagons}}}\]
+Please note that slopes are not taken into consideration.
+
+\subsubsection{Acceleration constants}
+\begin{tabular}{|c|r|r|}
+  \hline
+  Lever & $a_{\text{all}}$ & $a_{\text{locomotive}}$ \\
+  \hline
+  $0$ & $-10$ & $0$ \\
+  $1$ & $-3$ & $0$ \\
+  $2$ & $-0.5$ & $0$ \\
+  $3$ & $0$ & $0$ \\
+  $4$ & $0.5$ & $1.5$ \\
+  \hline
+\end{tabular}
+
+%%% Local Variables:
+%%% TeX-master: "a4manual"
+%%% End:
\ No newline at end of file
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