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\section{Comparison to Toy Models}  \label{sec:models}  In this section we compare the kinematic evidence for co-rotation discussed in the previous section to several simple "toy" models of satellite behavior. We begin by detailing how each toy model is constructed. constructed:  \begin{enumerate}  \item Isotropic model - In this case, each host may again have 2-5 satellites. Each satellite is independently assigned a random position and velocity, where the magnitude of the drawn from a uniform probability distribution from 0 km/s to 200 km/s. The model is subjected to a random rotation and oberved along the z direction, i.e. the z direction is taken to be the line of sight and the xy plane is taken to be the plane of the sky.