Galilean Transformation - Galilean Transformations

Galilean Transformations

The Galilean symmetries can be uniquely written as the composition of a rotation, a translation and a uniform motion of space-time. Let x represent a point in three-dimensional space, and t a point in one-dimensional time. A general point in space-time is given by an ordered pair (x,t). A uniform motion, with velocity v, is given by where v is in R3. A translation is given by where a in R3 and b in R. A rotation is given by where G : R3 → R3 is an orthogonal transformation. As a Lie group, the Galilean transformations have dimensions 10.