On the first Newton law, the existence of the reference system corresponding to the rest, and the Galilei group

In the Russian scientific literature, the authors carefully avoided mentioning the fact that Ernst Mach's assertion of 1904 about the meaninglessness of the concepts of uniform motion and absolute time in and of themselves has never been challenged in classical (not quantum) mechanics. Using hydrodynamics as an example, V. I. Arnold showed that a system of coordinates in which some finite volume of the medium is at rest exists almost always. We interpret this result as the existence of a system of coordinates in which all particles are at rest (the rest frame).