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author | Y. Wang <yw05@forksworld.de> | 2022-07-19 17:43:30 +0200 |
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committer | Y. Wang <yw05@forksworld.de> | 2022-07-19 17:52:57 +0200 |
commit | 5cc7f50bad779e4f4efb747a74bbce53a7e05cd3 (patch) | |
tree | b4e99693e34cec2b5161faaf4bdda9fab7a1e74a /assets/manual/physics.tex | |
parent | 3b167028b38753d776cec777efb07eae23e58a12 (diff) | |
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Split manual into multiple files
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diff --git a/assets/manual/physics.tex b/assets/manual/physics.tex new file mode 100644 index 0000000..5df11f9 --- /dev/null +++ b/assets/manual/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:
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