Galilean transformation

In physics, a 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. These transformations together with spatial rotations and translations in space and time form the inhomogeneous Galilean group (assumed throughout below). Without the translations in space and time the group is the homogeneous Galilean group. The Galilean group is the group of motions of Galilean relativity acting on the four dimensions of space and time, forming the Galilean geometry. This is the passive transformation point of view. In special relativity the homogeneous and inhomogeneous Galilean transformations are, respectively, replaced by the Lorentz transformations and Poincaré transformations; conversely, the group contraction in the classical limit c → ∞ of Poincaré transformations yields Galilean transformations.

The equations below are only physically valid in a Newtonian framework, and not applicable to coordinate systems moving relative to each other at speeds approaching the speed of light.

Galileo formulated these concepts in his description of uniform motion.^[1] The topic was motivated by his 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.