deletions | additions       diff --git a/physical model.tex b/physical model.tex  index 18e0e9e..5590f80 100644  --- a/physical model.tex  +++ b/physical model.tex 
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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:  \[  F_{a,b}(d_z) = b(1-\sqrt{\frac{d_z}{a}})_+ b\left(1-\sqrt{\frac{d_z}{a}}\right)_+  \]  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 $0$.