Principle of Galilean relativity

The laws of Newtonian mechanics have the same form in every inertial frame related by a Galilean transformation.

A dynamical symmetry under Galilean transformations. For an isolated pair with constant masses, a force law depending only on relative positions and relative velocities has this invariance. Equal-and-opposite forces alone do not imply it: their magnitude can depend on centre of mass velocity relative to a preferred frame.

For a Galilean transformation $t^{\prime }=t+b$, ${\mathbf{x}}^{\prime }=R\mathbf{x}-\mathbf{U}t+\mathbf{a}$, with constant rotation $R$ and boost $\mathbf{U}$, velocity transforms as ${\mathbf{v}}^{\prime }=R\mathbf{v}-\mathbf{U}$ and acceleration as ${\mathbf{a}}^{\prime }=R\mathbf{a}$. 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 ${\mathbf{F}}^{\prime }=R\mathbf{F}$. 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.