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authorY. Wang <yw05@forksworld.de>2022-07-08 13:30:48 +0200
committerY. Wang <yw05@forksworld.de>2022-07-08 13:30:48 +0200
commit3b167028b38753d776cec777efb07eae23e58a12 (patch)
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Minor improvements to the section on movement calculation
Diffstat (limited to 'assets/manual')
-rw-r--r--assets/manual/manual.tex14
1 files changed, 5 insertions, 9 deletions
diff --git a/assets/manual/manual.tex b/assets/manual/manual.tex
index fb36b93..0156169 100644
--- a/assets/manual/manual.tex
+++ b/assets/manual/manual.tex
@@ -1437,19 +1437,15 @@ This section is mainly intended as a reference that is provided for convenience.
\subsection{Movement}
-This section will use $x$ as the position and \( s = \Delta x \) as the distance.
-
\begin{align*}
- v(T) &= v_0 + \int_0^T a(t) dt \\
- x(T) &= x_0 + \int_0^T v(t) dt \\
- s(T) &= \Delta x = \int_0^T v(t) dt
+ v &= \int a\, dt \\
+ x &= \int v\, dt \\
\end{align*}
\subsubsection{Constant acceleration}
\begin{align*}
- v(T) &= v_0 + \int_0^T a(t)dt = v_0 + aT \\
- x(T) &= x_0 + \int_0^T v(t)dt = x_0 + v_0T + \frac{1}{2}aT^2 \\
- s(T) &= v_0T + \frac{1}{2}aT^2
+ 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:
@@ -1461,7 +1457,7 @@ In certain cases, the starting velocity $v_0$ and the target velocity $v_1$ are
\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 not that slopes are not taken into consideration.
+Please note that slopes are not taken into consideration.
\subsubsection{Acceleration constants}
\begin{tabular}{|c|r|r|}