Galilean transformation
with a rotation and/or a reflection, a constant translation, and a constant velocity called a boost.
A Galilean transformation between two reference frames and is given by
where is a rotation and/or a reflection, is a constant translation, and is a constant velocity, called a boost.
Preservation of inertial frames
Under a Galilean transformation,
Indeed, differentiating twice gives , and a rotation or reflection is invertible, so one acceleration vanishes exactly when the other does.
A frame related to an inertial frame by a Galilean transformation is therefore also an inertial frame. Acceleration is not relative: it has the same magnitude in all inertial frames.
Galilean group
The Galilean transformations form the Galilean group, often supplemented with time translations .
Related
Stated in
- Definition 1.3 (Galilean Transformation)§1 The Structure of the Newtonian Universe