dispersion is computed in the direction of each axis. For the previously mentioned quantities the stars considered for the calculations reside in a spherical volume of a radius $r_c$ of interest, centered on the satellite. The velocity dispersion of the system associated with radius $r_c$ is: $$\sigma_{\star}^{r_c} = \left( \frac{ \sigma_x^2 + \sigma_y^2 + \sigma_z^2 }{3} \right)^{1/2}$$ In order to compute the rotational velocity associated to the system, three cylindrical shell volumes are defined. Each of the volumes is defined with a central axis constrained to pass through the maximum density region of the object and to be parallel to a principal axis dimension. The inner and the outer radii of the volumes are 0.95 $r_c$ and 1.05 $r_c$.

For all the stars bound to the object and included in the previously defined volume, the component of their velocity tangential to any concentric circle centered on the axis of the cylinder is considered for the average. The resulting average is the velocity $v_{i,j}^{r_c}$, where $(i,j) \in {(x,y), (y,z), (z_x)}$.\
With the dispersion and rotation quantities determined, the ratio: $$\frac{v_{rot}^{r_{c}}}{\sigma_{\star}^{r_{c}}} = \frac{max \left( v_{x,y}^{r_c},v_{y,z}^{r_c},v_{z,x}^{r_c} \right)} { \sigma_{\star}^{r_c}}$$ can be used as another indicator of the degree of transformation from rotationally supported 