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?

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# Galilean principle of relativity

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