Galilean transformation

Lore & Background

Galileo formulated these concepts in his description of uniform motion. 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. Although the transformations are named for Galileo, it is the absolute time and space as conceived by Isaac Newton that provides their domain of definition. In essence, the Galilean transformations embody the intuitive notion of addition and subtraction of velocities as vectors.

Reader's Guide

The Galilean transformation is fundamental to Newtonian physics, providing the mathematical framework for relating observations made in different inertial frames moving at constant velocity relative to one another. The equations 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. In special relativity, the homogeneous and inhomogeneous Galilean transformations are replaced by the Lorentz transformations and Poincaré transformations; conversely, the group contraction in the classical limit c → ∞ of Poincaré transformations yields Galilean transformations. The Galilean group has dimension 10 and can be represented as a matrix group. Its subgroups include anisotropic transformations and isochronous transformations. The transformations are considered a shear mapping in linear algebra, described with a matrix acting on a vector. Though matrix representations are not strictly necessary, they provide the means for direct comparison to transformation methods in special relativity.

Did You Know?

• The Galilean transformation is used to transform between coordinates of two reference frames differing only by constant relative motion within Newtonian physics.
• The transformations together with spatial rotations and translations in space and time form the inhomogeneous Galilean group.
• In special relativity, Galilean transformations are replaced by Lorentz and Poincaré transformations.
• The Galilean group has dimension 10 and can be represented as a matrix group with spacetime events as vectors.