= Galilean covariance of Newton's second law
{c}
{title2=$\mathbf a'=R\mathbf a,\quad\mathbf F'=R\mathbf F$}
For a <Galilean transformation> $t'=t+b$, $\mathbf x'=R\mathbf x-\mathbf U t+\mathbf a$, with constant rotation $R$ and boost $\mathbf U$, <velocity> transforms as $\mathbf v'=R\mathbf v-\mathbf U$ and <acceleration> as $\mathbf a'=R\mathbf a$. With invariant inertial <mass>, <Newton's second law> retains its form only if the actual interaction laws and their physical background data transform to give $\mathbf F'=R\mathbf F$. Acceleration invariance alone does not prove covariance of an arbitrary force law. For example, resistance depends on velocity relative to a medium, whose <velocity> must transform too.
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