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Is there a Group that covers (classical) relative velocities?
I'm not very well versed in Abstract algebra and group theory, so this question might not make sense to begin with, but I got an idea when reading up on how to rigorously calculate relative velocities....
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Calculating relative velocity in three dimensional space
Given two points $\mathcal{A}$ and $\mathcal{B}$ in $\mathbb{R^3}$ whose position and velocity vectors are, respectively:
$$\mathbf{r_A}=\begin{pmatrix}r_{A_{x}}\\r_{A_{y}}\\r_{A_{z}}\end{pmatrix}$$
$$...
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