aboutsummaryrefslogtreecommitdiff
path: root/assets/manual/tex/physics.tex
diff options
context:
space:
mode:
Diffstat (limited to 'assets/manual/tex/physics.tex')
-rw-r--r--assets/manual/tex/physics.tex47
1 files changed, 47 insertions, 0 deletions
diff --git a/assets/manual/tex/physics.tex b/assets/manual/tex/physics.tex
new file mode 100644
index 0000000..5df11f9
--- /dev/null
+++ b/assets/manual/tex/physics.tex
@@ -0,0 +1,47 @@
+\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