A Galilean transformation consists of a rotation (in space), a boost (in space) and a translation (in space and time). This can be represented for homogeneous coordinates as(adsbygoogle = window.adsbygoogle || []).push({});

[tex]

\left[\begin{matrix}t'\\x'\\y'\\z'\\1\end{matrix}\right]=

\left[\begin{matrix}

1&0&0&0&t_{t}\\

u_{x}&R_{11}&R_{12}&R_{13}&t_{x}\\

u_{y}&R_{21}&R_{22}&R_{23}&t_{y}\\

u_{z}&R_{31}&R_{32}&R_{33}&t_{z}\\

0&0&0&0&1

\end{matrix}\right]

\cdot\left[\begin{matrix}t\\x\\y\\z\\1\end{matrix}\right]

[/tex]

To me there seem to be two principles of relativity in frames that are related by a Galilean transformation. The first says that all physical laws described in Galilean space-time have the same form in frames related by a Galilean transformation. Newton's second law of motion for example given by [itex]F=m.a[/itex] in one frame becomes [itex]F'=m.a'[/itex] in the second frame, while [itex]F[/itex] and [itex]F'[/itex] transform under a Galilean transformation.

The second says that all physical laws are the same in frames that are related by a Galilean transformation with [itex]R=id[/itex] (i.e. inertial frames of reference). Again Newton's second law of motion: [itex]F=F'[/itex] and [itex]a=a'[/itex].

Is this a correct understanding of Galilean relativity?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Galilean principle of relativity

**Physics Forums | Science Articles, Homework Help, Discussion**