- #1
kent davidge
- 933
- 56
It seems that there is a difference between Galilean transformations and (the transformations of the) Galilean group, for one thing: rotations.
The former is usually defined as the transformations ##\{\vec{x'} = \vec x - \vec v t, \ t' = t \}##, where ##\vec v## is the primed frame velocity relative to the first frame. On the other hand, rotations are also a possibility in going from one inertial frame to another, and they seem to be included in the Galilean Group.
So when people refer to Galilean Transformations do they mean the transformations that leave Newtons second law invariant? And when they are considering all transformations that leave the second law covariant then they are talking about the Galilean group?
The former is usually defined as the transformations ##\{\vec{x'} = \vec x - \vec v t, \ t' = t \}##, where ##\vec v## is the primed frame velocity relative to the first frame. On the other hand, rotations are also a possibility in going from one inertial frame to another, and they seem to be included in the Galilean Group.
So when people refer to Galilean Transformations do they mean the transformations that leave Newtons second law invariant? And when they are considering all transformations that leave the second law covariant then they are talking about the Galilean group?