The Galilean transformation is used to transform between the coordinates of two reference frames which differ only by constant relative motion within the constructs of Newtonian physics. This is the passive transformation point of view. The equations below, although apparently obvious, break down at speeds that approach the speed of light owing to physics described by relativity theory.
Galileo formulated these concepts in his description of uniform motion. The topic was motivated by Galileo's description of the motion of a ball rolling down a ramp, by which he measured the numerical value for the acceleration of gravity near the surface of the Earth.
Read more about Galilean Transformation: Translation, Galilean Transformations, Central Extension of The Galilean Group
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“Last came, and last did go,
The pilot of the Galilean lake.”
—John Milton (1608–1674)