The stated reference systems are mathematically defined using three dimensional Cartesian coordinates and sets of functions, and then systematically developed and contrasted. The linearity of the Lorentz transformation equations for special relativity is shown to follow directly from the definition of a Galilean inertial reference system.
Proceedings of the Iowa Academy of Science
©1960 Iowa Academy of Science, Inc.
Wolfson, C. Jake
"Newtonian and Galilean Reference Frames (of the Special Theory of Relativity) Defined and Compared by Elementary Mathematics,"
Proceedings of the Iowa Academy of Science, 67(1), 394-398.
Available at: https://scholarworks.uni.edu/pias/vol67/iss1/51