The Galilean transformation is a set of equations in classical mechanics that relate the space and time coordinates of two inertial frames of reference moving at constant velocity relative to each other.

The Galilean transformation assumes that time is absolute (the same in all reference frames). This assumption works well for objects moving at speeds much smaller than the speed of light, but breaks down at relativistic speeds where Lorentz transformations must be used instead.

Transformations

Consider two inertial frames and , where frame moves with constant velocity relative to frame . We assume that both frames have the same origin at .

Positional Transformation

The Galilean transformation can be expressed using position vectors:

Velocity Transformation