I started reading Landau's Mechanics book and was having some trouble understanding the Galilean Relativity Principle. What does Landau mean by saying space to be homogenous and isotropic and time is homogenous for an inertial observer? Also, how does he conclude using this that, the Lagrangian must be independent of $\vec{r}$, time and direction of $\vec{v}$ .
I am not understand what he wants to convey.
Also a side note, are there any lecture notes/books/videos etc. that explain in a bit more detail what Landau wishes to convey to the reader at times in his book.
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