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Sven Schmit edited physical model.tex
over 9 years ago
Commit id: b63788614191007be307a8bd01c2da51de0c9b7a
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All forces are calculated using the distance between the sheep and the other object, $z$, denoted by $d_z$, and are of the following form:
\[
F_{a,b}(d_z) =
b(1-\sqrt{d_z/a})_+ b(1-\sqrt{\frac{d_z}{a}})_+
\]
and where the direction of the force is given by the angle of $z$ relative to the sheep.
Note that the force function is paramaterized by $a$ and $b$, which have a simple interpetation: $a$ is the maximum distance of the force, and $b$ is the magnitude of the force when the distance is $0$.